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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.util;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import java.util.List;<a name="line.20"></a>
<FONT color="green">021</FONT>    import java.util.ArrayList;<a name="line.21"></a>
<FONT color="green">022</FONT>    import java.util.Comparator;<a name="line.22"></a>
<FONT color="green">023</FONT>    import java.util.Collections;<a name="line.23"></a>
<FONT color="green">024</FONT>    <a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.MathInternalError;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.exception.NonMonotonicSequenceException;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.exception.NotPositiveException;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.31"></a>
<FONT color="green">032</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.32"></a>
<FONT color="green">033</FONT>    import org.apache.commons.math3.exception.MathArithmeticException;<a name="line.33"></a>
<FONT color="green">034</FONT>    <a name="line.34"></a>
<FONT color="green">035</FONT>    /**<a name="line.35"></a>
<FONT color="green">036</FONT>     * Arrays utilities.<a name="line.36"></a>
<FONT color="green">037</FONT>     *<a name="line.37"></a>
<FONT color="green">038</FONT>     * @since 3.0<a name="line.38"></a>
<FONT color="green">039</FONT>     * @version $Id: MathArrays.java 1422313 2012-12-15 18:53:41Z psteitz $<a name="line.39"></a>
<FONT color="green">040</FONT>     */<a name="line.40"></a>
<FONT color="green">041</FONT>    public class MathArrays {<a name="line.41"></a>
<FONT color="green">042</FONT>        /** Factor used for splitting double numbers: n = 2^27 + 1 (i.e. {@value}). */<a name="line.42"></a>
<FONT color="green">043</FONT>        private static final int SPLIT_FACTOR = 0x8000001;<a name="line.43"></a>
<FONT color="green">044</FONT>    <a name="line.44"></a>
<FONT color="green">045</FONT>        /**<a name="line.45"></a>
<FONT color="green">046</FONT>         * Private constructor.<a name="line.46"></a>
<FONT color="green">047</FONT>         */<a name="line.47"></a>
<FONT color="green">048</FONT>        private MathArrays() {}<a name="line.48"></a>
<FONT color="green">049</FONT>    <a name="line.49"></a>
<FONT color="green">050</FONT>        /**<a name="line.50"></a>
<FONT color="green">051</FONT>         * Real-valued function that operate on an array or a part of it.<a name="line.51"></a>
<FONT color="green">052</FONT>         * @since 3.1<a name="line.52"></a>
<FONT color="green">053</FONT>         */<a name="line.53"></a>
<FONT color="green">054</FONT>        public interface Function {<a name="line.54"></a>
<FONT color="green">055</FONT>            /**<a name="line.55"></a>
<FONT color="green">056</FONT>             * Operates on an entire array.<a name="line.56"></a>
<FONT color="green">057</FONT>             *<a name="line.57"></a>
<FONT color="green">058</FONT>             * @param array Array to operate on.<a name="line.58"></a>
<FONT color="green">059</FONT>             * @return the result of the operation.<a name="line.59"></a>
<FONT color="green">060</FONT>             */<a name="line.60"></a>
<FONT color="green">061</FONT>            double evaluate(double[] array);<a name="line.61"></a>
<FONT color="green">062</FONT>            /**<a name="line.62"></a>
<FONT color="green">063</FONT>             * @param array Array to operate on.<a name="line.63"></a>
<FONT color="green">064</FONT>             * @param startIndex Index of the first element to take into account.<a name="line.64"></a>
<FONT color="green">065</FONT>             * @param numElements Number of elements to take into account.<a name="line.65"></a>
<FONT color="green">066</FONT>             * @return the result of the operation.<a name="line.66"></a>
<FONT color="green">067</FONT>             */<a name="line.67"></a>
<FONT color="green">068</FONT>            double evaluate(double[] array,<a name="line.68"></a>
<FONT color="green">069</FONT>                            int startIndex,<a name="line.69"></a>
<FONT color="green">070</FONT>                            int numElements);<a name="line.70"></a>
<FONT color="green">071</FONT>        }<a name="line.71"></a>
<FONT color="green">072</FONT>    <a name="line.72"></a>
<FONT color="green">073</FONT>        /**<a name="line.73"></a>
<FONT color="green">074</FONT>         * Creates an array whose contents will be the element-by-element<a name="line.74"></a>
<FONT color="green">075</FONT>         * addition of the arguments.<a name="line.75"></a>
<FONT color="green">076</FONT>         *<a name="line.76"></a>
<FONT color="green">077</FONT>         * @param a First term of the addition.<a name="line.77"></a>
<FONT color="green">078</FONT>         * @param b Second term of the addition.<a name="line.78"></a>
<FONT color="green">079</FONT>         * @return a new array {@code r} where {@code r[i] = a[i] + b[i]}.<a name="line.79"></a>
<FONT color="green">080</FONT>         * @throws DimensionMismatchException if the array lengths differ.<a name="line.80"></a>
<FONT color="green">081</FONT>         * @since 3.1<a name="line.81"></a>
<FONT color="green">082</FONT>         */<a name="line.82"></a>
<FONT color="green">083</FONT>        public static double[] ebeAdd(double[] a,<a name="line.83"></a>
<FONT color="green">084</FONT>                                      double[] b) {<a name="line.84"></a>
<FONT color="green">085</FONT>            if (a.length != b.length) {<a name="line.85"></a>
<FONT color="green">086</FONT>                throw new DimensionMismatchException(a.length, b.length);<a name="line.86"></a>
<FONT color="green">087</FONT>            }<a name="line.87"></a>
<FONT color="green">088</FONT>    <a name="line.88"></a>
<FONT color="green">089</FONT>            final double[] result = a.clone();<a name="line.89"></a>
<FONT color="green">090</FONT>            for (int i = 0; i &lt; a.length; i++) {<a name="line.90"></a>
<FONT color="green">091</FONT>                result[i] += b[i];<a name="line.91"></a>
<FONT color="green">092</FONT>            }<a name="line.92"></a>
<FONT color="green">093</FONT>            return result;<a name="line.93"></a>
<FONT color="green">094</FONT>        }<a name="line.94"></a>
<FONT color="green">095</FONT>        /**<a name="line.95"></a>
<FONT color="green">096</FONT>         * Creates an array whose contents will be the element-by-element<a name="line.96"></a>
<FONT color="green">097</FONT>         * subtraction of the second argument from the first.<a name="line.97"></a>
<FONT color="green">098</FONT>         *<a name="line.98"></a>
<FONT color="green">099</FONT>         * @param a First term.<a name="line.99"></a>
<FONT color="green">100</FONT>         * @param b Element to be subtracted.<a name="line.100"></a>
<FONT color="green">101</FONT>         * @return a new array {@code r} where {@code r[i] = a[i] - b[i]}.<a name="line.101"></a>
<FONT color="green">102</FONT>         * @throws DimensionMismatchException if the array lengths differ.<a name="line.102"></a>
<FONT color="green">103</FONT>         * @since 3.1<a name="line.103"></a>
<FONT color="green">104</FONT>         */<a name="line.104"></a>
<FONT color="green">105</FONT>        public static double[] ebeSubtract(double[] a,<a name="line.105"></a>
<FONT color="green">106</FONT>                                           double[] b) {<a name="line.106"></a>
<FONT color="green">107</FONT>            if (a.length != b.length) {<a name="line.107"></a>
<FONT color="green">108</FONT>                throw new DimensionMismatchException(a.length, b.length);<a name="line.108"></a>
<FONT color="green">109</FONT>            }<a name="line.109"></a>
<FONT color="green">110</FONT>    <a name="line.110"></a>
<FONT color="green">111</FONT>            final double[] result = a.clone();<a name="line.111"></a>
<FONT color="green">112</FONT>            for (int i = 0; i &lt; a.length; i++) {<a name="line.112"></a>
<FONT color="green">113</FONT>                result[i] -= b[i];<a name="line.113"></a>
<FONT color="green">114</FONT>            }<a name="line.114"></a>
<FONT color="green">115</FONT>            return result;<a name="line.115"></a>
<FONT color="green">116</FONT>        }<a name="line.116"></a>
<FONT color="green">117</FONT>        /**<a name="line.117"></a>
<FONT color="green">118</FONT>         * Creates an array whose contents will be the element-by-element<a name="line.118"></a>
<FONT color="green">119</FONT>         * multiplication of the arguments.<a name="line.119"></a>
<FONT color="green">120</FONT>         *<a name="line.120"></a>
<FONT color="green">121</FONT>         * @param a First factor of the multiplication.<a name="line.121"></a>
<FONT color="green">122</FONT>         * @param b Second factor of the multiplication.<a name="line.122"></a>
<FONT color="green">123</FONT>         * @return a new array {@code r} where {@code r[i] = a[i] * b[i]}.<a name="line.123"></a>
<FONT color="green">124</FONT>         * @throws DimensionMismatchException if the array lengths differ.<a name="line.124"></a>
<FONT color="green">125</FONT>         * @since 3.1<a name="line.125"></a>
<FONT color="green">126</FONT>         */<a name="line.126"></a>
<FONT color="green">127</FONT>        public static double[] ebeMultiply(double[] a,<a name="line.127"></a>
<FONT color="green">128</FONT>                                           double[] b) {<a name="line.128"></a>
<FONT color="green">129</FONT>            if (a.length != b.length) {<a name="line.129"></a>
<FONT color="green">130</FONT>                throw new DimensionMismatchException(a.length, b.length);<a name="line.130"></a>
<FONT color="green">131</FONT>            }<a name="line.131"></a>
<FONT color="green">132</FONT>    <a name="line.132"></a>
<FONT color="green">133</FONT>            final double[] result = a.clone();<a name="line.133"></a>
<FONT color="green">134</FONT>            for (int i = 0; i &lt; a.length; i++) {<a name="line.134"></a>
<FONT color="green">135</FONT>                result[i] *= b[i];<a name="line.135"></a>
<FONT color="green">136</FONT>            }<a name="line.136"></a>
<FONT color="green">137</FONT>            return result;<a name="line.137"></a>
<FONT color="green">138</FONT>        }<a name="line.138"></a>
<FONT color="green">139</FONT>        /**<a name="line.139"></a>
<FONT color="green">140</FONT>         * Creates an array whose contents will be the element-by-element<a name="line.140"></a>
<FONT color="green">141</FONT>         * division of the first argument by the second.<a name="line.141"></a>
<FONT color="green">142</FONT>         *<a name="line.142"></a>
<FONT color="green">143</FONT>         * @param a Numerator of the division.<a name="line.143"></a>
<FONT color="green">144</FONT>         * @param b Denominator of the division.<a name="line.144"></a>
<FONT color="green">145</FONT>         * @return a new array {@code r} where {@code r[i] = a[i] / b[i]}.<a name="line.145"></a>
<FONT color="green">146</FONT>         * @throws DimensionMismatchException if the array lengths differ.<a name="line.146"></a>
<FONT color="green">147</FONT>         * @since 3.1<a name="line.147"></a>
<FONT color="green">148</FONT>         */<a name="line.148"></a>
<FONT color="green">149</FONT>        public static double[] ebeDivide(double[] a,<a name="line.149"></a>
<FONT color="green">150</FONT>                                         double[] b) {<a name="line.150"></a>
<FONT color="green">151</FONT>            if (a.length != b.length) {<a name="line.151"></a>
<FONT color="green">152</FONT>                throw new DimensionMismatchException(a.length, b.length);<a name="line.152"></a>
<FONT color="green">153</FONT>            }<a name="line.153"></a>
<FONT color="green">154</FONT>    <a name="line.154"></a>
<FONT color="green">155</FONT>            final double[] result = a.clone();<a name="line.155"></a>
<FONT color="green">156</FONT>            for (int i = 0; i &lt; a.length; i++) {<a name="line.156"></a>
<FONT color="green">157</FONT>                result[i] /= b[i];<a name="line.157"></a>
<FONT color="green">158</FONT>            }<a name="line.158"></a>
<FONT color="green">159</FONT>            return result;<a name="line.159"></a>
<FONT color="green">160</FONT>        }<a name="line.160"></a>
<FONT color="green">161</FONT>    <a name="line.161"></a>
<FONT color="green">162</FONT>        /**<a name="line.162"></a>
<FONT color="green">163</FONT>         * Calculates the L&lt;sub&gt;1&lt;/sub&gt; (sum of abs) distance between two points.<a name="line.163"></a>
<FONT color="green">164</FONT>         *<a name="line.164"></a>
<FONT color="green">165</FONT>         * @param p1 the first point<a name="line.165"></a>
<FONT color="green">166</FONT>         * @param p2 the second point<a name="line.166"></a>
<FONT color="green">167</FONT>         * @return the L&lt;sub&gt;1&lt;/sub&gt; distance between the two points<a name="line.167"></a>
<FONT color="green">168</FONT>         */<a name="line.168"></a>
<FONT color="green">169</FONT>        public static double distance1(double[] p1, double[] p2) {<a name="line.169"></a>
<FONT color="green">170</FONT>            double sum = 0;<a name="line.170"></a>
<FONT color="green">171</FONT>            for (int i = 0; i &lt; p1.length; i++) {<a name="line.171"></a>
<FONT color="green">172</FONT>                sum += FastMath.abs(p1[i] - p2[i]);<a name="line.172"></a>
<FONT color="green">173</FONT>            }<a name="line.173"></a>
<FONT color="green">174</FONT>            return sum;<a name="line.174"></a>
<FONT color="green">175</FONT>        }<a name="line.175"></a>
<FONT color="green">176</FONT>    <a name="line.176"></a>
<FONT color="green">177</FONT>        /**<a name="line.177"></a>
<FONT color="green">178</FONT>         * Calculates the L&lt;sub&gt;1&lt;/sub&gt; (sum of abs) distance between two points.<a name="line.178"></a>
<FONT color="green">179</FONT>         *<a name="line.179"></a>
<FONT color="green">180</FONT>         * @param p1 the first point<a name="line.180"></a>
<FONT color="green">181</FONT>         * @param p2 the second point<a name="line.181"></a>
<FONT color="green">182</FONT>         * @return the L&lt;sub&gt;1&lt;/sub&gt; distance between the two points<a name="line.182"></a>
<FONT color="green">183</FONT>         */<a name="line.183"></a>
<FONT color="green">184</FONT>        public static int distance1(int[] p1, int[] p2) {<a name="line.184"></a>
<FONT color="green">185</FONT>          int sum = 0;<a name="line.185"></a>
<FONT color="green">186</FONT>          for (int i = 0; i &lt; p1.length; i++) {<a name="line.186"></a>
<FONT color="green">187</FONT>              sum += FastMath.abs(p1[i] - p2[i]);<a name="line.187"></a>
<FONT color="green">188</FONT>          }<a name="line.188"></a>
<FONT color="green">189</FONT>          return sum;<a name="line.189"></a>
<FONT color="green">190</FONT>        }<a name="line.190"></a>
<FONT color="green">191</FONT>    <a name="line.191"></a>
<FONT color="green">192</FONT>        /**<a name="line.192"></a>
<FONT color="green">193</FONT>         * Calculates the L&lt;sub&gt;2&lt;/sub&gt; (Euclidean) distance between two points.<a name="line.193"></a>
<FONT color="green">194</FONT>         *<a name="line.194"></a>
<FONT color="green">195</FONT>         * @param p1 the first point<a name="line.195"></a>
<FONT color="green">196</FONT>         * @param p2 the second point<a name="line.196"></a>
<FONT color="green">197</FONT>         * @return the L&lt;sub&gt;2&lt;/sub&gt; distance between the two points<a name="line.197"></a>
<FONT color="green">198</FONT>         */<a name="line.198"></a>
<FONT color="green">199</FONT>        public static double distance(double[] p1, double[] p2) {<a name="line.199"></a>
<FONT color="green">200</FONT>            double sum = 0;<a name="line.200"></a>
<FONT color="green">201</FONT>            for (int i = 0; i &lt; p1.length; i++) {<a name="line.201"></a>
<FONT color="green">202</FONT>                final double dp = p1[i] - p2[i];<a name="line.202"></a>
<FONT color="green">203</FONT>                sum += dp * dp;<a name="line.203"></a>
<FONT color="green">204</FONT>            }<a name="line.204"></a>
<FONT color="green">205</FONT>            return FastMath.sqrt(sum);<a name="line.205"></a>
<FONT color="green">206</FONT>        }<a name="line.206"></a>
<FONT color="green">207</FONT>    <a name="line.207"></a>
<FONT color="green">208</FONT>        /**<a name="line.208"></a>
<FONT color="green">209</FONT>         * Calculates the L&lt;sub&gt;2&lt;/sub&gt; (Euclidean) distance between two points.<a name="line.209"></a>
<FONT color="green">210</FONT>         *<a name="line.210"></a>
<FONT color="green">211</FONT>         * @param p1 the first point<a name="line.211"></a>
<FONT color="green">212</FONT>         * @param p2 the second point<a name="line.212"></a>
<FONT color="green">213</FONT>         * @return the L&lt;sub&gt;2&lt;/sub&gt; distance between the two points<a name="line.213"></a>
<FONT color="green">214</FONT>         */<a name="line.214"></a>
<FONT color="green">215</FONT>        public static double distance(int[] p1, int[] p2) {<a name="line.215"></a>
<FONT color="green">216</FONT>          double sum = 0;<a name="line.216"></a>
<FONT color="green">217</FONT>          for (int i = 0; i &lt; p1.length; i++) {<a name="line.217"></a>
<FONT color="green">218</FONT>              final double dp = p1[i] - p2[i];<a name="line.218"></a>
<FONT color="green">219</FONT>              sum += dp * dp;<a name="line.219"></a>
<FONT color="green">220</FONT>          }<a name="line.220"></a>
<FONT color="green">221</FONT>          return FastMath.sqrt(sum);<a name="line.221"></a>
<FONT color="green">222</FONT>        }<a name="line.222"></a>
<FONT color="green">223</FONT>    <a name="line.223"></a>
<FONT color="green">224</FONT>        /**<a name="line.224"></a>
<FONT color="green">225</FONT>         * Calculates the L&lt;sub&gt;&amp;infin;&lt;/sub&gt; (max of abs) distance between two points.<a name="line.225"></a>
<FONT color="green">226</FONT>         *<a name="line.226"></a>
<FONT color="green">227</FONT>         * @param p1 the first point<a name="line.227"></a>
<FONT color="green">228</FONT>         * @param p2 the second point<a name="line.228"></a>
<FONT color="green">229</FONT>         * @return the L&lt;sub&gt;&amp;infin;&lt;/sub&gt; distance between the two points<a name="line.229"></a>
<FONT color="green">230</FONT>         */<a name="line.230"></a>
<FONT color="green">231</FONT>        public static double distanceInf(double[] p1, double[] p2) {<a name="line.231"></a>
<FONT color="green">232</FONT>            double max = 0;<a name="line.232"></a>
<FONT color="green">233</FONT>            for (int i = 0; i &lt; p1.length; i++) {<a name="line.233"></a>
<FONT color="green">234</FONT>                max = FastMath.max(max, FastMath.abs(p1[i] - p2[i]));<a name="line.234"></a>
<FONT color="green">235</FONT>            }<a name="line.235"></a>
<FONT color="green">236</FONT>            return max;<a name="line.236"></a>
<FONT color="green">237</FONT>        }<a name="line.237"></a>
<FONT color="green">238</FONT>    <a name="line.238"></a>
<FONT color="green">239</FONT>        /**<a name="line.239"></a>
<FONT color="green">240</FONT>         * Calculates the L&lt;sub&gt;&amp;infin;&lt;/sub&gt; (max of abs) distance between two points.<a name="line.240"></a>
<FONT color="green">241</FONT>         *<a name="line.241"></a>
<FONT color="green">242</FONT>         * @param p1 the first point<a name="line.242"></a>
<FONT color="green">243</FONT>         * @param p2 the second point<a name="line.243"></a>
<FONT color="green">244</FONT>         * @return the L&lt;sub&gt;&amp;infin;&lt;/sub&gt; distance between the two points<a name="line.244"></a>
<FONT color="green">245</FONT>         */<a name="line.245"></a>
<FONT color="green">246</FONT>        public static int distanceInf(int[] p1, int[] p2) {<a name="line.246"></a>
<FONT color="green">247</FONT>            int max = 0;<a name="line.247"></a>
<FONT color="green">248</FONT>            for (int i = 0; i &lt; p1.length; i++) {<a name="line.248"></a>
<FONT color="green">249</FONT>                max = FastMath.max(max, FastMath.abs(p1[i] - p2[i]));<a name="line.249"></a>
<FONT color="green">250</FONT>            }<a name="line.250"></a>
<FONT color="green">251</FONT>            return max;<a name="line.251"></a>
<FONT color="green">252</FONT>        }<a name="line.252"></a>
<FONT color="green">253</FONT>    <a name="line.253"></a>
<FONT color="green">254</FONT>        /**<a name="line.254"></a>
<FONT color="green">255</FONT>         * Specification of ordering direction.<a name="line.255"></a>
<FONT color="green">256</FONT>         */<a name="line.256"></a>
<FONT color="green">257</FONT>        public static enum OrderDirection {<a name="line.257"></a>
<FONT color="green">258</FONT>            /** Constant for increasing direction. */<a name="line.258"></a>
<FONT color="green">259</FONT>            INCREASING,<a name="line.259"></a>
<FONT color="green">260</FONT>            /** Constant for decreasing direction. */<a name="line.260"></a>
<FONT color="green">261</FONT>            DECREASING<a name="line.261"></a>
<FONT color="green">262</FONT>        }<a name="line.262"></a>
<FONT color="green">263</FONT>    <a name="line.263"></a>
<FONT color="green">264</FONT>        /**<a name="line.264"></a>
<FONT color="green">265</FONT>         * Check that an array is monotonically increasing or decreasing.<a name="line.265"></a>
<FONT color="green">266</FONT>         *<a name="line.266"></a>
<FONT color="green">267</FONT>         * @param &lt;T&gt; the type of the elements in the specified array<a name="line.267"></a>
<FONT color="green">268</FONT>         * @param val Values.<a name="line.268"></a>
<FONT color="green">269</FONT>         * @param dir Ordering direction.<a name="line.269"></a>
<FONT color="green">270</FONT>         * @param strict Whether the order should be strict.<a name="line.270"></a>
<FONT color="green">271</FONT>         * @return {@code true} if sorted, {@code false} otherwise.<a name="line.271"></a>
<FONT color="green">272</FONT>         */<a name="line.272"></a>
<FONT color="green">273</FONT>        public static  &lt;T extends Comparable&lt;? super T&gt;&gt; boolean isMonotonic(T[] val,<a name="line.273"></a>
<FONT color="green">274</FONT>                                          OrderDirection dir,<a name="line.274"></a>
<FONT color="green">275</FONT>                                          boolean strict) {<a name="line.275"></a>
<FONT color="green">276</FONT>            T previous = val[0];<a name="line.276"></a>
<FONT color="green">277</FONT>            final int max = val.length;<a name="line.277"></a>
<FONT color="green">278</FONT>            for (int i = 1; i &lt; max; i++) {<a name="line.278"></a>
<FONT color="green">279</FONT>                final int comp;<a name="line.279"></a>
<FONT color="green">280</FONT>                switch (dir) {<a name="line.280"></a>
<FONT color="green">281</FONT>                case INCREASING:<a name="line.281"></a>
<FONT color="green">282</FONT>                    comp = previous.compareTo(val[i]);<a name="line.282"></a>
<FONT color="green">283</FONT>                    if (strict) {<a name="line.283"></a>
<FONT color="green">284</FONT>                        if (comp &gt;= 0) {<a name="line.284"></a>
<FONT color="green">285</FONT>                            return false;<a name="line.285"></a>
<FONT color="green">286</FONT>                        }<a name="line.286"></a>
<FONT color="green">287</FONT>                    } else {<a name="line.287"></a>
<FONT color="green">288</FONT>                        if (comp &gt; 0) {<a name="line.288"></a>
<FONT color="green">289</FONT>                            return false;<a name="line.289"></a>
<FONT color="green">290</FONT>                        }<a name="line.290"></a>
<FONT color="green">291</FONT>                    }<a name="line.291"></a>
<FONT color="green">292</FONT>                    break;<a name="line.292"></a>
<FONT color="green">293</FONT>                case DECREASING:<a name="line.293"></a>
<FONT color="green">294</FONT>                    comp = val[i].compareTo(previous);<a name="line.294"></a>
<FONT color="green">295</FONT>                    if (strict) {<a name="line.295"></a>
<FONT color="green">296</FONT>                        if (comp &gt;= 0) {<a name="line.296"></a>
<FONT color="green">297</FONT>                            return false;<a name="line.297"></a>
<FONT color="green">298</FONT>                        }<a name="line.298"></a>
<FONT color="green">299</FONT>                    } else {<a name="line.299"></a>
<FONT color="green">300</FONT>                        if (comp &gt; 0) {<a name="line.300"></a>
<FONT color="green">301</FONT>                           return false;<a name="line.301"></a>
<FONT color="green">302</FONT>                        }<a name="line.302"></a>
<FONT color="green">303</FONT>                    }<a name="line.303"></a>
<FONT color="green">304</FONT>                    break;<a name="line.304"></a>
<FONT color="green">305</FONT>                default:<a name="line.305"></a>
<FONT color="green">306</FONT>                    // Should never happen.<a name="line.306"></a>
<FONT color="green">307</FONT>                    throw new MathInternalError();<a name="line.307"></a>
<FONT color="green">308</FONT>                }<a name="line.308"></a>
<FONT color="green">309</FONT>    <a name="line.309"></a>
<FONT color="green">310</FONT>                previous = val[i];<a name="line.310"></a>
<FONT color="green">311</FONT>            }<a name="line.311"></a>
<FONT color="green">312</FONT>            return true;<a name="line.312"></a>
<FONT color="green">313</FONT>        }<a name="line.313"></a>
<FONT color="green">314</FONT>    <a name="line.314"></a>
<FONT color="green">315</FONT>        /**<a name="line.315"></a>
<FONT color="green">316</FONT>         * Check that an array is monotonically increasing or decreasing.<a name="line.316"></a>
<FONT color="green">317</FONT>         *<a name="line.317"></a>
<FONT color="green">318</FONT>         * @param val Values.<a name="line.318"></a>
<FONT color="green">319</FONT>         * @param dir Ordering direction.<a name="line.319"></a>
<FONT color="green">320</FONT>         * @param strict Whether the order should be strict.<a name="line.320"></a>
<FONT color="green">321</FONT>         * @return {@code true} if sorted, {@code false} otherwise.<a name="line.321"></a>
<FONT color="green">322</FONT>         */<a name="line.322"></a>
<FONT color="green">323</FONT>        public static boolean isMonotonic(double[] val,<a name="line.323"></a>
<FONT color="green">324</FONT>                                          OrderDirection dir,<a name="line.324"></a>
<FONT color="green">325</FONT>                                          boolean strict) {<a name="line.325"></a>
<FONT color="green">326</FONT>            return checkOrder(val, dir, strict, false);<a name="line.326"></a>
<FONT color="green">327</FONT>        }<a name="line.327"></a>
<FONT color="green">328</FONT>    <a name="line.328"></a>
<FONT color="green">329</FONT>        /**<a name="line.329"></a>
<FONT color="green">330</FONT>         * Check that the given array is sorted.<a name="line.330"></a>
<FONT color="green">331</FONT>         *<a name="line.331"></a>
<FONT color="green">332</FONT>         * @param val Values.<a name="line.332"></a>
<FONT color="green">333</FONT>         * @param dir Ordering direction.<a name="line.333"></a>
<FONT color="green">334</FONT>         * @param strict Whether the order should be strict.<a name="line.334"></a>
<FONT color="green">335</FONT>         * @param abort Whether to throw an exception if the check fails.<a name="line.335"></a>
<FONT color="green">336</FONT>         * @return {@code true} if the array is sorted.<a name="line.336"></a>
<FONT color="green">337</FONT>         * @throws NonMonotonicSequenceException if the array is not sorted<a name="line.337"></a>
<FONT color="green">338</FONT>         * and {@code abort} is {@code true}.<a name="line.338"></a>
<FONT color="green">339</FONT>         */<a name="line.339"></a>
<FONT color="green">340</FONT>        public static boolean checkOrder(double[] val, OrderDirection dir,<a name="line.340"></a>
<FONT color="green">341</FONT>                                         boolean strict, boolean abort)<a name="line.341"></a>
<FONT color="green">342</FONT>            throws NonMonotonicSequenceException {<a name="line.342"></a>
<FONT color="green">343</FONT>            double previous = val[0];<a name="line.343"></a>
<FONT color="green">344</FONT>            final int max = val.length;<a name="line.344"></a>
<FONT color="green">345</FONT>    <a name="line.345"></a>
<FONT color="green">346</FONT>            int index;<a name="line.346"></a>
<FONT color="green">347</FONT>            ITEM:<a name="line.347"></a>
<FONT color="green">348</FONT>            for (index = 1; index &lt; max; index++) {<a name="line.348"></a>
<FONT color="green">349</FONT>                switch (dir) {<a name="line.349"></a>
<FONT color="green">350</FONT>                case INCREASING:<a name="line.350"></a>
<FONT color="green">351</FONT>                    if (strict) {<a name="line.351"></a>
<FONT color="green">352</FONT>                        if (val[index] &lt;= previous) {<a name="line.352"></a>
<FONT color="green">353</FONT>                            break ITEM;<a name="line.353"></a>
<FONT color="green">354</FONT>                        }<a name="line.354"></a>
<FONT color="green">355</FONT>                    } else {<a name="line.355"></a>
<FONT color="green">356</FONT>                        if (val[index] &lt; previous) {<a name="line.356"></a>
<FONT color="green">357</FONT>                            break ITEM;<a name="line.357"></a>
<FONT color="green">358</FONT>                        }<a name="line.358"></a>
<FONT color="green">359</FONT>                    }<a name="line.359"></a>
<FONT color="green">360</FONT>                    break;<a name="line.360"></a>
<FONT color="green">361</FONT>                case DECREASING:<a name="line.361"></a>
<FONT color="green">362</FONT>                    if (strict) {<a name="line.362"></a>
<FONT color="green">363</FONT>                        if (val[index] &gt;= previous) {<a name="line.363"></a>
<FONT color="green">364</FONT>                            break ITEM;<a name="line.364"></a>
<FONT color="green">365</FONT>                        }<a name="line.365"></a>
<FONT color="green">366</FONT>                    } else {<a name="line.366"></a>
<FONT color="green">367</FONT>                        if (val[index] &gt; previous) {<a name="line.367"></a>
<FONT color="green">368</FONT>                            break ITEM;<a name="line.368"></a>
<FONT color="green">369</FONT>                        }<a name="line.369"></a>
<FONT color="green">370</FONT>                    }<a name="line.370"></a>
<FONT color="green">371</FONT>                    break;<a name="line.371"></a>
<FONT color="green">372</FONT>                default:<a name="line.372"></a>
<FONT color="green">373</FONT>                    // Should never happen.<a name="line.373"></a>
<FONT color="green">374</FONT>                    throw new MathInternalError();<a name="line.374"></a>
<FONT color="green">375</FONT>                }<a name="line.375"></a>
<FONT color="green">376</FONT>    <a name="line.376"></a>
<FONT color="green">377</FONT>                previous = val[index];<a name="line.377"></a>
<FONT color="green">378</FONT>            }<a name="line.378"></a>
<FONT color="green">379</FONT>    <a name="line.379"></a>
<FONT color="green">380</FONT>            if (index == max) {<a name="line.380"></a>
<FONT color="green">381</FONT>                // Loop completed.<a name="line.381"></a>
<FONT color="green">382</FONT>                return true;<a name="line.382"></a>
<FONT color="green">383</FONT>            }<a name="line.383"></a>
<FONT color="green">384</FONT>    <a name="line.384"></a>
<FONT color="green">385</FONT>            // Loop early exit means wrong ordering.<a name="line.385"></a>
<FONT color="green">386</FONT>            if (abort) {<a name="line.386"></a>
<FONT color="green">387</FONT>                throw new NonMonotonicSequenceException(val[index], previous, index, dir, strict);<a name="line.387"></a>
<FONT color="green">388</FONT>            } else {<a name="line.388"></a>
<FONT color="green">389</FONT>                return false;<a name="line.389"></a>
<FONT color="green">390</FONT>            }<a name="line.390"></a>
<FONT color="green">391</FONT>        }<a name="line.391"></a>
<FONT color="green">392</FONT>    <a name="line.392"></a>
<FONT color="green">393</FONT>        /**<a name="line.393"></a>
<FONT color="green">394</FONT>         * Check that the given array is sorted.<a name="line.394"></a>
<FONT color="green">395</FONT>         *<a name="line.395"></a>
<FONT color="green">396</FONT>         * @param val Values.<a name="line.396"></a>
<FONT color="green">397</FONT>         * @param dir Ordering direction.<a name="line.397"></a>
<FONT color="green">398</FONT>         * @param strict Whether the order should be strict.<a name="line.398"></a>
<FONT color="green">399</FONT>         * @throws NonMonotonicSequenceException if the array is not sorted.<a name="line.399"></a>
<FONT color="green">400</FONT>         * @since 2.2<a name="line.400"></a>
<FONT color="green">401</FONT>         */<a name="line.401"></a>
<FONT color="green">402</FONT>        public static void checkOrder(double[] val, OrderDirection dir,<a name="line.402"></a>
<FONT color="green">403</FONT>                                      boolean strict) throws NonMonotonicSequenceException {<a name="line.403"></a>
<FONT color="green">404</FONT>            checkOrder(val, dir, strict, true);<a name="line.404"></a>
<FONT color="green">405</FONT>        }<a name="line.405"></a>
<FONT color="green">406</FONT>    <a name="line.406"></a>
<FONT color="green">407</FONT>        /**<a name="line.407"></a>
<FONT color="green">408</FONT>         * Check that the given array is sorted in strictly increasing order.<a name="line.408"></a>
<FONT color="green">409</FONT>         *<a name="line.409"></a>
<FONT color="green">410</FONT>         * @param val Values.<a name="line.410"></a>
<FONT color="green">411</FONT>         * @throws NonMonotonicSequenceException if the array is not sorted.<a name="line.411"></a>
<FONT color="green">412</FONT>         * @since 2.2<a name="line.412"></a>
<FONT color="green">413</FONT>         */<a name="line.413"></a>
<FONT color="green">414</FONT>        public static void checkOrder(double[] val) throws NonMonotonicSequenceException {<a name="line.414"></a>
<FONT color="green">415</FONT>            checkOrder(val, OrderDirection.INCREASING, true);<a name="line.415"></a>
<FONT color="green">416</FONT>        }<a name="line.416"></a>
<FONT color="green">417</FONT>    <a name="line.417"></a>
<FONT color="green">418</FONT>        /**<a name="line.418"></a>
<FONT color="green">419</FONT>         * Throws DimensionMismatchException if the input array is not rectangular.<a name="line.419"></a>
<FONT color="green">420</FONT>         *<a name="line.420"></a>
<FONT color="green">421</FONT>         * @param in array to be tested<a name="line.421"></a>
<FONT color="green">422</FONT>         * @throws NullArgumentException if input array is null<a name="line.422"></a>
<FONT color="green">423</FONT>         * @throws DimensionMismatchException if input array is not rectangular<a name="line.423"></a>
<FONT color="green">424</FONT>         * @since 3.1<a name="line.424"></a>
<FONT color="green">425</FONT>         */<a name="line.425"></a>
<FONT color="green">426</FONT>        public static void checkRectangular(final long[][] in)<a name="line.426"></a>
<FONT color="green">427</FONT>            throws NullArgumentException, DimensionMismatchException {<a name="line.427"></a>
<FONT color="green">428</FONT>            MathUtils.checkNotNull(in);<a name="line.428"></a>
<FONT color="green">429</FONT>            for (int i = 1; i &lt; in.length; i++) {<a name="line.429"></a>
<FONT color="green">430</FONT>                if (in[i].length != in[0].length) {<a name="line.430"></a>
<FONT color="green">431</FONT>                    throw new DimensionMismatchException(<a name="line.431"></a>
<FONT color="green">432</FONT>                            LocalizedFormats.DIFFERENT_ROWS_LENGTHS,<a name="line.432"></a>
<FONT color="green">433</FONT>                            in[i].length, in[0].length);<a name="line.433"></a>
<FONT color="green">434</FONT>                }<a name="line.434"></a>
<FONT color="green">435</FONT>            }<a name="line.435"></a>
<FONT color="green">436</FONT>        }<a name="line.436"></a>
<FONT color="green">437</FONT>    <a name="line.437"></a>
<FONT color="green">438</FONT>        /**<a name="line.438"></a>
<FONT color="green">439</FONT>         * Check that all entries of the input array are strictly positive.<a name="line.439"></a>
<FONT color="green">440</FONT>         *<a name="line.440"></a>
<FONT color="green">441</FONT>         * @param in Array to be tested<a name="line.441"></a>
<FONT color="green">442</FONT>         * @throws NotStrictlyPositiveException if any entries of the array are not<a name="line.442"></a>
<FONT color="green">443</FONT>         * strictly positive.<a name="line.443"></a>
<FONT color="green">444</FONT>         * @since 3.1<a name="line.444"></a>
<FONT color="green">445</FONT>         */<a name="line.445"></a>
<FONT color="green">446</FONT>        public static void checkPositive(final double[] in)<a name="line.446"></a>
<FONT color="green">447</FONT>            throws NotStrictlyPositiveException {<a name="line.447"></a>
<FONT color="green">448</FONT>            for (int i = 0; i &lt; in.length; i++) {<a name="line.448"></a>
<FONT color="green">449</FONT>                if (in[i] &lt;= 0) {<a name="line.449"></a>
<FONT color="green">450</FONT>                    throw new NotStrictlyPositiveException(in[i]);<a name="line.450"></a>
<FONT color="green">451</FONT>                }<a name="line.451"></a>
<FONT color="green">452</FONT>            }<a name="line.452"></a>
<FONT color="green">453</FONT>        }<a name="line.453"></a>
<FONT color="green">454</FONT>    <a name="line.454"></a>
<FONT color="green">455</FONT>        /**<a name="line.455"></a>
<FONT color="green">456</FONT>         * Check that all entries of the input array are &gt;= 0.<a name="line.456"></a>
<FONT color="green">457</FONT>         *<a name="line.457"></a>
<FONT color="green">458</FONT>         * @param in Array to be tested<a name="line.458"></a>
<FONT color="green">459</FONT>         * @throws NotPositiveException if any array entries are less than 0.<a name="line.459"></a>
<FONT color="green">460</FONT>         * @since 3.1<a name="line.460"></a>
<FONT color="green">461</FONT>         */<a name="line.461"></a>
<FONT color="green">462</FONT>        public static void checkNonNegative(final long[] in)<a name="line.462"></a>
<FONT color="green">463</FONT>            throws NotPositiveException {<a name="line.463"></a>
<FONT color="green">464</FONT>            for (int i = 0; i &lt; in.length; i++) {<a name="line.464"></a>
<FONT color="green">465</FONT>                if (in[i] &lt; 0) {<a name="line.465"></a>
<FONT color="green">466</FONT>                    throw new NotPositiveException(in[i]);<a name="line.466"></a>
<FONT color="green">467</FONT>                }<a name="line.467"></a>
<FONT color="green">468</FONT>            }<a name="line.468"></a>
<FONT color="green">469</FONT>        }<a name="line.469"></a>
<FONT color="green">470</FONT>    <a name="line.470"></a>
<FONT color="green">471</FONT>        /**<a name="line.471"></a>
<FONT color="green">472</FONT>         * Check all entries of the input array are &gt;= 0.<a name="line.472"></a>
<FONT color="green">473</FONT>         *<a name="line.473"></a>
<FONT color="green">474</FONT>         * @param in Array to be tested<a name="line.474"></a>
<FONT color="green">475</FONT>         * @throws NotPositiveException if any array entries are less than 0.<a name="line.475"></a>
<FONT color="green">476</FONT>         * @since 3.1<a name="line.476"></a>
<FONT color="green">477</FONT>         */<a name="line.477"></a>
<FONT color="green">478</FONT>        public static void checkNonNegative(final long[][] in)<a name="line.478"></a>
<FONT color="green">479</FONT>            throws NotPositiveException {<a name="line.479"></a>
<FONT color="green">480</FONT>            for (int i = 0; i &lt; in.length; i ++) {<a name="line.480"></a>
<FONT color="green">481</FONT>                for (int j = 0; j &lt; in[i].length; j++) {<a name="line.481"></a>
<FONT color="green">482</FONT>                    if (in[i][j] &lt; 0) {<a name="line.482"></a>
<FONT color="green">483</FONT>                        throw new NotPositiveException(in[i][j]);<a name="line.483"></a>
<FONT color="green">484</FONT>                    }<a name="line.484"></a>
<FONT color="green">485</FONT>                }<a name="line.485"></a>
<FONT color="green">486</FONT>            }<a name="line.486"></a>
<FONT color="green">487</FONT>        }<a name="line.487"></a>
<FONT color="green">488</FONT>    <a name="line.488"></a>
<FONT color="green">489</FONT>        /**<a name="line.489"></a>
<FONT color="green">490</FONT>         * Returns the Cartesian norm (2-norm), handling both overflow and underflow.<a name="line.490"></a>
<FONT color="green">491</FONT>         * Translation of the minpack enorm subroutine.<a name="line.491"></a>
<FONT color="green">492</FONT>         *<a name="line.492"></a>
<FONT color="green">493</FONT>         * The redistribution policy for MINPACK is available<a name="line.493"></a>
<FONT color="green">494</FONT>         * &lt;a href="http://www.netlib.org/minpack/disclaimer"&gt;here&lt;/a&gt;, for<a name="line.494"></a>
<FONT color="green">495</FONT>         * convenience, it is reproduced below.&lt;/p&gt;<a name="line.495"></a>
<FONT color="green">496</FONT>         *<a name="line.496"></a>
<FONT color="green">497</FONT>         * &lt;table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0"&gt;<a name="line.497"></a>
<FONT color="green">498</FONT>         * &lt;tr&gt;&lt;td&gt;<a name="line.498"></a>
<FONT color="green">499</FONT>         *    Minpack Copyright Notice (1999) University of Chicago.<a name="line.499"></a>
<FONT color="green">500</FONT>         *    All rights reserved<a name="line.500"></a>
<FONT color="green">501</FONT>         * &lt;/td&gt;&lt;/tr&gt;<a name="line.501"></a>
<FONT color="green">502</FONT>         * &lt;tr&gt;&lt;td&gt;<a name="line.502"></a>
<FONT color="green">503</FONT>         * Redistribution and use in source and binary forms, with or without<a name="line.503"></a>
<FONT color="green">504</FONT>         * modification, are permitted provided that the following conditions<a name="line.504"></a>
<FONT color="green">505</FONT>         * are met:<a name="line.505"></a>
<FONT color="green">506</FONT>         * &lt;ol&gt;<a name="line.506"></a>
<FONT color="green">507</FONT>         *  &lt;li&gt;Redistributions of source code must retain the above copyright<a name="line.507"></a>
<FONT color="green">508</FONT>         *      notice, this list of conditions and the following disclaimer.&lt;/li&gt;<a name="line.508"></a>
<FONT color="green">509</FONT>         * &lt;li&gt;Redistributions in binary form must reproduce the above<a name="line.509"></a>
<FONT color="green">510</FONT>         *     copyright notice, this list of conditions and the following<a name="line.510"></a>
<FONT color="green">511</FONT>         *     disclaimer in the documentation and/or other materials provided<a name="line.511"></a>
<FONT color="green">512</FONT>         *     with the distribution.&lt;/li&gt;<a name="line.512"></a>
<FONT color="green">513</FONT>         * &lt;li&gt;The end-user documentation included with the redistribution, if any,<a name="line.513"></a>
<FONT color="green">514</FONT>         *     must include the following acknowledgment:<a name="line.514"></a>
<FONT color="green">515</FONT>         *     {@code This product includes software developed by the University of<a name="line.515"></a>
<FONT color="green">516</FONT>         *           Chicago, as Operator of Argonne National Laboratory.}<a name="line.516"></a>
<FONT color="green">517</FONT>         *     Alternately, this acknowledgment may appear in the software itself,<a name="line.517"></a>
<FONT color="green">518</FONT>         *     if and wherever such third-party acknowledgments normally appear.&lt;/li&gt;<a name="line.518"></a>
<FONT color="green">519</FONT>         * &lt;li&gt;&lt;strong&gt;WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"<a name="line.519"></a>
<FONT color="green">520</FONT>         *     WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE<a name="line.520"></a>
<FONT color="green">521</FONT>         *     UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND<a name="line.521"></a>
<FONT color="green">522</FONT>         *     THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR<a name="line.522"></a>
<FONT color="green">523</FONT>         *     IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES<a name="line.523"></a>
<FONT color="green">524</FONT>         *     OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE<a name="line.524"></a>
<FONT color="green">525</FONT>         *     OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY<a name="line.525"></a>
<FONT color="green">526</FONT>         *     OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR<a name="line.526"></a>
<FONT color="green">527</FONT>         *     USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF<a name="line.527"></a>
<FONT color="green">528</FONT>         *     THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)<a name="line.528"></a>
<FONT color="green">529</FONT>         *     DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION<a name="line.529"></a>
<FONT color="green">530</FONT>         *     UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL<a name="line.530"></a>
<FONT color="green">531</FONT>         *     BE CORRECTED.&lt;/strong&gt;&lt;/li&gt;<a name="line.531"></a>
<FONT color="green">532</FONT>         * &lt;li&gt;&lt;strong&gt;LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT<a name="line.532"></a>
<FONT color="green">533</FONT>         *     HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF<a name="line.533"></a>
<FONT color="green">534</FONT>         *     ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,<a name="line.534"></a>
<FONT color="green">535</FONT>         *     INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF<a name="line.535"></a>
<FONT color="green">536</FONT>         *     ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF<a name="line.536"></a>
<FONT color="green">537</FONT>         *     PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER<a name="line.537"></a>
<FONT color="green">538</FONT>         *     SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT<a name="line.538"></a>
<FONT color="green">539</FONT>         *     (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,<a name="line.539"></a>
<FONT color="green">540</FONT>         *     EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE<a name="line.540"></a>
<FONT color="green">541</FONT>         *     POSSIBILITY OF SUCH LOSS OR DAMAGES.&lt;/strong&gt;&lt;/li&gt;<a name="line.541"></a>
<FONT color="green">542</FONT>         * &lt;ol&gt;&lt;/td&gt;&lt;/tr&gt;<a name="line.542"></a>
<FONT color="green">543</FONT>         * &lt;/table&gt;<a name="line.543"></a>
<FONT color="green">544</FONT>         *<a name="line.544"></a>
<FONT color="green">545</FONT>         * @param v Vector of doubles.<a name="line.545"></a>
<FONT color="green">546</FONT>         * @return the 2-norm of the vector.<a name="line.546"></a>
<FONT color="green">547</FONT>         * @since 2.2<a name="line.547"></a>
<FONT color="green">548</FONT>         */<a name="line.548"></a>
<FONT color="green">549</FONT>        public static double safeNorm(double[] v) {<a name="line.549"></a>
<FONT color="green">550</FONT>            double rdwarf = 3.834e-20;<a name="line.550"></a>
<FONT color="green">551</FONT>            double rgiant = 1.304e+19;<a name="line.551"></a>
<FONT color="green">552</FONT>            double s1 = 0;<a name="line.552"></a>
<FONT color="green">553</FONT>            double s2 = 0;<a name="line.553"></a>
<FONT color="green">554</FONT>            double s3 = 0;<a name="line.554"></a>
<FONT color="green">555</FONT>            double x1max = 0;<a name="line.555"></a>
<FONT color="green">556</FONT>            double x3max = 0;<a name="line.556"></a>
<FONT color="green">557</FONT>            double floatn = v.length;<a name="line.557"></a>
<FONT color="green">558</FONT>            double agiant = rgiant / floatn;<a name="line.558"></a>
<FONT color="green">559</FONT>            for (int i = 0; i &lt; v.length; i++) {<a name="line.559"></a>
<FONT color="green">560</FONT>                double xabs = Math.abs(v[i]);<a name="line.560"></a>
<FONT color="green">561</FONT>                if (xabs &lt; rdwarf || xabs &gt; agiant) {<a name="line.561"></a>
<FONT color="green">562</FONT>                    if (xabs &gt; rdwarf) {<a name="line.562"></a>
<FONT color="green">563</FONT>                        if (xabs &gt; x1max) {<a name="line.563"></a>
<FONT color="green">564</FONT>                            double r = x1max / xabs;<a name="line.564"></a>
<FONT color="green">565</FONT>                            s1= 1 + s1 * r * r;<a name="line.565"></a>
<FONT color="green">566</FONT>                            x1max = xabs;<a name="line.566"></a>
<FONT color="green">567</FONT>                        } else {<a name="line.567"></a>
<FONT color="green">568</FONT>                            double r = xabs / x1max;<a name="line.568"></a>
<FONT color="green">569</FONT>                            s1 += r * r;<a name="line.569"></a>
<FONT color="green">570</FONT>                        }<a name="line.570"></a>
<FONT color="green">571</FONT>                    } else {<a name="line.571"></a>
<FONT color="green">572</FONT>                        if (xabs &gt; x3max) {<a name="line.572"></a>
<FONT color="green">573</FONT>                            double r = x3max / xabs;<a name="line.573"></a>
<FONT color="green">574</FONT>                            s3= 1 + s3 * r * r;<a name="line.574"></a>
<FONT color="green">575</FONT>                            x3max = xabs;<a name="line.575"></a>
<FONT color="green">576</FONT>                        } else {<a name="line.576"></a>
<FONT color="green">577</FONT>                            if (xabs != 0) {<a name="line.577"></a>
<FONT color="green">578</FONT>                                double r = xabs / x3max;<a name="line.578"></a>
<FONT color="green">579</FONT>                                s3 += r * r;<a name="line.579"></a>
<FONT color="green">580</FONT>                            }<a name="line.580"></a>
<FONT color="green">581</FONT>                        }<a name="line.581"></a>
<FONT color="green">582</FONT>                    }<a name="line.582"></a>
<FONT color="green">583</FONT>                } else {<a name="line.583"></a>
<FONT color="green">584</FONT>                    s2 += xabs * xabs;<a name="line.584"></a>
<FONT color="green">585</FONT>                }<a name="line.585"></a>
<FONT color="green">586</FONT>            }<a name="line.586"></a>
<FONT color="green">587</FONT>            double norm;<a name="line.587"></a>
<FONT color="green">588</FONT>            if (s1 != 0) {<a name="line.588"></a>
<FONT color="green">589</FONT>                norm = x1max * Math.sqrt(s1 + (s2 / x1max) / x1max);<a name="line.589"></a>
<FONT color="green">590</FONT>            } else {<a name="line.590"></a>
<FONT color="green">591</FONT>                if (s2 == 0) {<a name="line.591"></a>
<FONT color="green">592</FONT>                    norm = x3max * Math.sqrt(s3);<a name="line.592"></a>
<FONT color="green">593</FONT>                } else {<a name="line.593"></a>
<FONT color="green">594</FONT>                    if (s2 &gt;= x3max) {<a name="line.594"></a>
<FONT color="green">595</FONT>                        norm = Math.sqrt(s2 * (1 + (x3max / s2) * (x3max * s3)));<a name="line.595"></a>
<FONT color="green">596</FONT>                    } else {<a name="line.596"></a>
<FONT color="green">597</FONT>                        norm = Math.sqrt(x3max * ((s2 / x3max) + (x3max * s3)));<a name="line.597"></a>
<FONT color="green">598</FONT>                    }<a name="line.598"></a>
<FONT color="green">599</FONT>                }<a name="line.599"></a>
<FONT color="green">600</FONT>            }<a name="line.600"></a>
<FONT color="green">601</FONT>            return norm;<a name="line.601"></a>
<FONT color="green">602</FONT>        }<a name="line.602"></a>
<FONT color="green">603</FONT>    <a name="line.603"></a>
<FONT color="green">604</FONT>        /**<a name="line.604"></a>
<FONT color="green">605</FONT>         * Sort an array in ascending order in place and perform the same reordering<a name="line.605"></a>
<FONT color="green">606</FONT>         * of entries on other arrays. For example, if<a name="line.606"></a>
<FONT color="green">607</FONT>         * {@code x = [3, 1, 2], y = [1, 2, 3]} and {@code z = [0, 5, 7]}, then<a name="line.607"></a>
<FONT color="green">608</FONT>         * {@code sortInPlace(x, y, z)} will update {@code x} to {@code [1, 2, 3]},<a name="line.608"></a>
<FONT color="green">609</FONT>         * {@code y} to {@code [2, 3, 1]} and {@code z} to {@code [5, 7, 0]}.<a name="line.609"></a>
<FONT color="green">610</FONT>         *<a name="line.610"></a>
<FONT color="green">611</FONT>         * @param x Array to be sorted and used as a pattern for permutation<a name="line.611"></a>
<FONT color="green">612</FONT>         * of the other arrays.<a name="line.612"></a>
<FONT color="green">613</FONT>         * @param yList Set of arrays whose permutations of entries will follow<a name="line.613"></a>
<FONT color="green">614</FONT>         * those performed on {@code x}.<a name="line.614"></a>
<FONT color="green">615</FONT>         * @throws DimensionMismatchException if any {@code y} is not the same<a name="line.615"></a>
<FONT color="green">616</FONT>         * size as {@code x}.<a name="line.616"></a>
<FONT color="green">617</FONT>         * @throws NullArgumentException if {@code x} or any {@code y} is null.<a name="line.617"></a>
<FONT color="green">618</FONT>         * @since 3.0<a name="line.618"></a>
<FONT color="green">619</FONT>         */<a name="line.619"></a>
<FONT color="green">620</FONT>        public static void sortInPlace(double[] x, double[] ... yList)<a name="line.620"></a>
<FONT color="green">621</FONT>            throws DimensionMismatchException, NullArgumentException {<a name="line.621"></a>
<FONT color="green">622</FONT>            sortInPlace(x, OrderDirection.INCREASING, yList);<a name="line.622"></a>
<FONT color="green">623</FONT>        }<a name="line.623"></a>
<FONT color="green">624</FONT>    <a name="line.624"></a>
<FONT color="green">625</FONT>        /**<a name="line.625"></a>
<FONT color="green">626</FONT>         * Sort an array in place and perform the same reordering of entries on<a name="line.626"></a>
<FONT color="green">627</FONT>         * other arrays.  This method works the same as the other<a name="line.627"></a>
<FONT color="green">628</FONT>         * {@link #sortInPlace(double[], double[][]) sortInPlace} method, but<a name="line.628"></a>
<FONT color="green">629</FONT>         * allows the order of the sort to be provided in the {@code dir}<a name="line.629"></a>
<FONT color="green">630</FONT>         * parameter.<a name="line.630"></a>
<FONT color="green">631</FONT>         *<a name="line.631"></a>
<FONT color="green">632</FONT>         * @param x Array to be sorted and used as a pattern for permutation<a name="line.632"></a>
<FONT color="green">633</FONT>         * of the other arrays.<a name="line.633"></a>
<FONT color="green">634</FONT>         * @param dir Order direction.<a name="line.634"></a>
<FONT color="green">635</FONT>         * @param yList Set of arrays whose permutations of entries will follow<a name="line.635"></a>
<FONT color="green">636</FONT>         * those performed on {@code x}.<a name="line.636"></a>
<FONT color="green">637</FONT>         * @throws DimensionMismatchException if any {@code y} is not the same<a name="line.637"></a>
<FONT color="green">638</FONT>         * size as {@code x}.<a name="line.638"></a>
<FONT color="green">639</FONT>         * @throws NullArgumentException if {@code x} or any {@code y} is null<a name="line.639"></a>
<FONT color="green">640</FONT>         * @since 3.0<a name="line.640"></a>
<FONT color="green">641</FONT>         */<a name="line.641"></a>
<FONT color="green">642</FONT>        public static void sortInPlace(double[] x,<a name="line.642"></a>
<FONT color="green">643</FONT>                                       final OrderDirection dir,<a name="line.643"></a>
<FONT color="green">644</FONT>                                       double[] ... yList)<a name="line.644"></a>
<FONT color="green">645</FONT>            throws NullArgumentException, DimensionMismatchException {<a name="line.645"></a>
<FONT color="green">646</FONT>            if (x == null) {<a name="line.646"></a>
<FONT color="green">647</FONT>                throw new NullArgumentException();<a name="line.647"></a>
<FONT color="green">648</FONT>            }<a name="line.648"></a>
<FONT color="green">649</FONT>    <a name="line.649"></a>
<FONT color="green">650</FONT>            final int len = x.length;<a name="line.650"></a>
<FONT color="green">651</FONT>            final List&lt;Pair&lt;Double, double[]&gt;&gt; list<a name="line.651"></a>
<FONT color="green">652</FONT>                = new ArrayList&lt;Pair&lt;Double, double[]&gt;&gt;(len);<a name="line.652"></a>
<FONT color="green">653</FONT>    <a name="line.653"></a>
<FONT color="green">654</FONT>            final int yListLen = yList.length;<a name="line.654"></a>
<FONT color="green">655</FONT>            for (int i = 0; i &lt; len; i++) {<a name="line.655"></a>
<FONT color="green">656</FONT>                final double[] yValues = new double[yListLen];<a name="line.656"></a>
<FONT color="green">657</FONT>                for (int j = 0; j &lt; yListLen; j++) {<a name="line.657"></a>
<FONT color="green">658</FONT>                    double[] y = yList[j];<a name="line.658"></a>
<FONT color="green">659</FONT>                    if (y == null) {<a name="line.659"></a>
<FONT color="green">660</FONT>                        throw new NullArgumentException();<a name="line.660"></a>
<FONT color="green">661</FONT>                    }<a name="line.661"></a>
<FONT color="green">662</FONT>                    if (y.length != len) {<a name="line.662"></a>
<FONT color="green">663</FONT>                        throw new DimensionMismatchException(y.length, len);<a name="line.663"></a>
<FONT color="green">664</FONT>                    }<a name="line.664"></a>
<FONT color="green">665</FONT>                    yValues[j] = y[i];<a name="line.665"></a>
<FONT color="green">666</FONT>                }<a name="line.666"></a>
<FONT color="green">667</FONT>                list.add(new Pair&lt;Double, double[]&gt;(x[i], yValues));<a name="line.667"></a>
<FONT color="green">668</FONT>            }<a name="line.668"></a>
<FONT color="green">669</FONT>    <a name="line.669"></a>
<FONT color="green">670</FONT>            final Comparator&lt;Pair&lt;Double, double[]&gt;&gt; comp<a name="line.670"></a>
<FONT color="green">671</FONT>                = new Comparator&lt;Pair&lt;Double, double[]&gt;&gt;() {<a name="line.671"></a>
<FONT color="green">672</FONT>                public int compare(Pair&lt;Double, double[]&gt; o1,<a name="line.672"></a>
<FONT color="green">673</FONT>                                   Pair&lt;Double, double[]&gt; o2) {<a name="line.673"></a>
<FONT color="green">674</FONT>                    int val;<a name="line.674"></a>
<FONT color="green">675</FONT>                    switch (dir) {<a name="line.675"></a>
<FONT color="green">676</FONT>                    case INCREASING:<a name="line.676"></a>
<FONT color="green">677</FONT>                        val = o1.getKey().compareTo(o2.getKey());<a name="line.677"></a>
<FONT color="green">678</FONT>                    break;<a name="line.678"></a>
<FONT color="green">679</FONT>                    case DECREASING:<a name="line.679"></a>
<FONT color="green">680</FONT>                        val = o2.getKey().compareTo(o1.getKey());<a name="line.680"></a>
<FONT color="green">681</FONT>                    break;<a name="line.681"></a>
<FONT color="green">682</FONT>                    default:<a name="line.682"></a>
<FONT color="green">683</FONT>                        // Should never happen.<a name="line.683"></a>
<FONT color="green">684</FONT>                        throw new MathInternalError();<a name="line.684"></a>
<FONT color="green">685</FONT>                    }<a name="line.685"></a>
<FONT color="green">686</FONT>                    return val;<a name="line.686"></a>
<FONT color="green">687</FONT>                }<a name="line.687"></a>
<FONT color="green">688</FONT>            };<a name="line.688"></a>
<FONT color="green">689</FONT>    <a name="line.689"></a>
<FONT color="green">690</FONT>            Collections.sort(list, comp);<a name="line.690"></a>
<FONT color="green">691</FONT>    <a name="line.691"></a>
<FONT color="green">692</FONT>            for (int i = 0; i &lt; len; i++) {<a name="line.692"></a>
<FONT color="green">693</FONT>                final Pair&lt;Double, double[]&gt; e = list.get(i);<a name="line.693"></a>
<FONT color="green">694</FONT>                x[i] = e.getKey();<a name="line.694"></a>
<FONT color="green">695</FONT>                final double[] yValues = e.getValue();<a name="line.695"></a>
<FONT color="green">696</FONT>                for (int j = 0; j &lt; yListLen; j++) {<a name="line.696"></a>
<FONT color="green">697</FONT>                    yList[j][i] = yValues[j];<a name="line.697"></a>
<FONT color="green">698</FONT>                }<a name="line.698"></a>
<FONT color="green">699</FONT>            }<a name="line.699"></a>
<FONT color="green">700</FONT>        }<a name="line.700"></a>
<FONT color="green">701</FONT>    <a name="line.701"></a>
<FONT color="green">702</FONT>        /**<a name="line.702"></a>
<FONT color="green">703</FONT>         * Creates a copy of the {@code source} array.<a name="line.703"></a>
<FONT color="green">704</FONT>         *<a name="line.704"></a>
<FONT color="green">705</FONT>         * @param source Array to be copied.<a name="line.705"></a>
<FONT color="green">706</FONT>         * @return the copied array.<a name="line.706"></a>
<FONT color="green">707</FONT>         */<a name="line.707"></a>
<FONT color="green">708</FONT>         public static int[] copyOf(int[] source) {<a name="line.708"></a>
<FONT color="green">709</FONT>             return copyOf(source, source.length);<a name="line.709"></a>
<FONT color="green">710</FONT>         }<a name="line.710"></a>
<FONT color="green">711</FONT>    <a name="line.711"></a>
<FONT color="green">712</FONT>        /**<a name="line.712"></a>
<FONT color="green">713</FONT>         * Creates a copy of the {@code source} array.<a name="line.713"></a>
<FONT color="green">714</FONT>         *<a name="line.714"></a>
<FONT color="green">715</FONT>         * @param source Array to be copied.<a name="line.715"></a>
<FONT color="green">716</FONT>         * @return the copied array.<a name="line.716"></a>
<FONT color="green">717</FONT>         */<a name="line.717"></a>
<FONT color="green">718</FONT>         public static double[] copyOf(double[] source) {<a name="line.718"></a>
<FONT color="green">719</FONT>             return copyOf(source, source.length);<a name="line.719"></a>
<FONT color="green">720</FONT>         }<a name="line.720"></a>
<FONT color="green">721</FONT>    <a name="line.721"></a>
<FONT color="green">722</FONT>        /**<a name="line.722"></a>
<FONT color="green">723</FONT>         * Creates a copy of the {@code source} array.<a name="line.723"></a>
<FONT color="green">724</FONT>         *<a name="line.724"></a>
<FONT color="green">725</FONT>         * @param source Array to be copied.<a name="line.725"></a>
<FONT color="green">726</FONT>         * @param len Number of entries to copy. If smaller then the source<a name="line.726"></a>
<FONT color="green">727</FONT>         * length, the copy will be truncated, if larger it will padded with<a name="line.727"></a>
<FONT color="green">728</FONT>         * zeroes.<a name="line.728"></a>
<FONT color="green">729</FONT>         * @return the copied array.<a name="line.729"></a>
<FONT color="green">730</FONT>         */<a name="line.730"></a>
<FONT color="green">731</FONT>        public static int[] copyOf(int[] source, int len) {<a name="line.731"></a>
<FONT color="green">732</FONT>             final int[] output = new int[len];<a name="line.732"></a>
<FONT color="green">733</FONT>             System.arraycopy(source, 0, output, 0, FastMath.min(len, source.length));<a name="line.733"></a>
<FONT color="green">734</FONT>             return output;<a name="line.734"></a>
<FONT color="green">735</FONT>         }<a name="line.735"></a>
<FONT color="green">736</FONT>    <a name="line.736"></a>
<FONT color="green">737</FONT>        /**<a name="line.737"></a>
<FONT color="green">738</FONT>         * Creates a copy of the {@code source} array.<a name="line.738"></a>
<FONT color="green">739</FONT>         *<a name="line.739"></a>
<FONT color="green">740</FONT>         * @param source Array to be copied.<a name="line.740"></a>
<FONT color="green">741</FONT>         * @param len Number of entries to copy. If smaller then the source<a name="line.741"></a>
<FONT color="green">742</FONT>         * length, the copy will be truncated, if larger it will padded with<a name="line.742"></a>
<FONT color="green">743</FONT>         * zeroes.<a name="line.743"></a>
<FONT color="green">744</FONT>         * @return the copied array.<a name="line.744"></a>
<FONT color="green">745</FONT>         */<a name="line.745"></a>
<FONT color="green">746</FONT>        public static double[] copyOf(double[] source, int len) {<a name="line.746"></a>
<FONT color="green">747</FONT>             final double[] output = new double[len];<a name="line.747"></a>
<FONT color="green">748</FONT>             System.arraycopy(source, 0, output, 0, FastMath.min(len, source.length));<a name="line.748"></a>
<FONT color="green">749</FONT>             return output;<a name="line.749"></a>
<FONT color="green">750</FONT>         }<a name="line.750"></a>
<FONT color="green">751</FONT>    <a name="line.751"></a>
<FONT color="green">752</FONT>        /**<a name="line.752"></a>
<FONT color="green">753</FONT>         * Compute a linear combination accurately.<a name="line.753"></a>
<FONT color="green">754</FONT>         * This method computes the sum of the products<a name="line.754"></a>
<FONT color="green">755</FONT>         * &lt;code&gt;a&lt;sub&gt;i&lt;/sub&gt; b&lt;sub&gt;i&lt;/sub&gt;&lt;/code&gt; to high accuracy.<a name="line.755"></a>
<FONT color="green">756</FONT>         * It does so by using specific multiplication and addition algorithms to<a name="line.756"></a>
<FONT color="green">757</FONT>         * preserve accuracy and reduce cancellation effects.<a name="line.757"></a>
<FONT color="green">758</FONT>         * &lt;br/&gt;<a name="line.758"></a>
<FONT color="green">759</FONT>         * It is based on the 2005 paper<a name="line.759"></a>
<FONT color="green">760</FONT>         * &lt;a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547"&gt;<a name="line.760"></a>
<FONT color="green">761</FONT>         * Accurate Sum and Dot Product&lt;/a&gt; by Takeshi Ogita, Siegfried M. Rump,<a name="line.761"></a>
<FONT color="green">762</FONT>         * and Shin'ichi Oishi published in SIAM J. Sci. Comput.<a name="line.762"></a>
<FONT color="green">763</FONT>         *<a name="line.763"></a>
<FONT color="green">764</FONT>         * @param a Factors.<a name="line.764"></a>
<FONT color="green">765</FONT>         * @param b Factors.<a name="line.765"></a>
<FONT color="green">766</FONT>         * @return &lt;code&gt;&amp;Sigma;&lt;sub&gt;i&lt;/sub&gt; a&lt;sub&gt;i&lt;/sub&gt; b&lt;sub&gt;i&lt;/sub&gt;&lt;/code&gt;.<a name="line.766"></a>
<FONT color="green">767</FONT>         * @throws DimensionMismatchException if arrays dimensions don't match<a name="line.767"></a>
<FONT color="green">768</FONT>         */<a name="line.768"></a>
<FONT color="green">769</FONT>        public static double linearCombination(final double[] a, final double[] b)<a name="line.769"></a>
<FONT color="green">770</FONT>            throws DimensionMismatchException {<a name="line.770"></a>
<FONT color="green">771</FONT>            final int len = a.length;<a name="line.771"></a>
<FONT color="green">772</FONT>            if (len != b.length) {<a name="line.772"></a>
<FONT color="green">773</FONT>                throw new DimensionMismatchException(len, b.length);<a name="line.773"></a>
<FONT color="green">774</FONT>            }<a name="line.774"></a>
<FONT color="green">775</FONT>    <a name="line.775"></a>
<FONT color="green">776</FONT>            final double[] prodHigh = new double[len];<a name="line.776"></a>
<FONT color="green">777</FONT>            double prodLowSum = 0;<a name="line.777"></a>
<FONT color="green">778</FONT>    <a name="line.778"></a>
<FONT color="green">779</FONT>            for (int i = 0; i &lt; len; i++) {<a name="line.779"></a>
<FONT color="green">780</FONT>                final double ai = a[i];<a name="line.780"></a>
<FONT color="green">781</FONT>                final double ca = SPLIT_FACTOR * ai;<a name="line.781"></a>
<FONT color="green">782</FONT>                final double aHigh = ca - (ca - ai);<a name="line.782"></a>
<FONT color="green">783</FONT>                final double aLow = ai - aHigh;<a name="line.783"></a>
<FONT color="green">784</FONT>    <a name="line.784"></a>
<FONT color="green">785</FONT>                final double bi = b[i];<a name="line.785"></a>
<FONT color="green">786</FONT>                final double cb = SPLIT_FACTOR * bi;<a name="line.786"></a>
<FONT color="green">787</FONT>                final double bHigh = cb - (cb - bi);<a name="line.787"></a>
<FONT color="green">788</FONT>                final double bLow = bi - bHigh;<a name="line.788"></a>
<FONT color="green">789</FONT>                prodHigh[i] = ai * bi;<a name="line.789"></a>
<FONT color="green">790</FONT>                final double prodLow = aLow * bLow - (((prodHigh[i] -<a name="line.790"></a>
<FONT color="green">791</FONT>                                                        aHigh * bHigh) -<a name="line.791"></a>
<FONT color="green">792</FONT>                                                       aLow * bHigh) -<a name="line.792"></a>
<FONT color="green">793</FONT>                                                      aHigh * bLow);<a name="line.793"></a>
<FONT color="green">794</FONT>                prodLowSum += prodLow;<a name="line.794"></a>
<FONT color="green">795</FONT>            }<a name="line.795"></a>
<FONT color="green">796</FONT>    <a name="line.796"></a>
<FONT color="green">797</FONT>    <a name="line.797"></a>
<FONT color="green">798</FONT>            final double prodHighCur = prodHigh[0];<a name="line.798"></a>
<FONT color="green">799</FONT>            double prodHighNext = prodHigh[1];<a name="line.799"></a>
<FONT color="green">800</FONT>            double sHighPrev = prodHighCur + prodHighNext;<a name="line.800"></a>
<FONT color="green">801</FONT>            double sPrime = sHighPrev - prodHighNext;<a name="line.801"></a>
<FONT color="green">802</FONT>            double sLowSum = (prodHighNext - (sHighPrev - sPrime)) + (prodHighCur - sPrime);<a name="line.802"></a>
<FONT color="green">803</FONT>    <a name="line.803"></a>
<FONT color="green">804</FONT>            final int lenMinusOne = len - 1;<a name="line.804"></a>
<FONT color="green">805</FONT>            for (int i = 1; i &lt; lenMinusOne; i++) {<a name="line.805"></a>
<FONT color="green">806</FONT>                prodHighNext = prodHigh[i + 1];<a name="line.806"></a>
<FONT color="green">807</FONT>                final double sHighCur = sHighPrev + prodHighNext;<a name="line.807"></a>
<FONT color="green">808</FONT>                sPrime = sHighCur - prodHighNext;<a name="line.808"></a>
<FONT color="green">809</FONT>                sLowSum += (prodHighNext - (sHighCur - sPrime)) + (sHighPrev - sPrime);<a name="line.809"></a>
<FONT color="green">810</FONT>                sHighPrev = sHighCur;<a name="line.810"></a>
<FONT color="green">811</FONT>            }<a name="line.811"></a>
<FONT color="green">812</FONT>    <a name="line.812"></a>
<FONT color="green">813</FONT>            double result = sHighPrev + (prodLowSum + sLowSum);<a name="line.813"></a>
<FONT color="green">814</FONT>    <a name="line.814"></a>
<FONT color="green">815</FONT>            if (Double.isNaN(result)) {<a name="line.815"></a>
<FONT color="green">816</FONT>                // either we have split infinite numbers or some coefficients were NaNs,<a name="line.816"></a>
<FONT color="green">817</FONT>                // just rely on the naive implementation and let IEEE754 handle this<a name="line.817"></a>
<FONT color="green">818</FONT>                result = 0;<a name="line.818"></a>
<FONT color="green">819</FONT>                for (int i = 0; i &lt; len; ++i) {<a name="line.819"></a>
<FONT color="green">820</FONT>                    result += a[i] * b[i];<a name="line.820"></a>
<FONT color="green">821</FONT>                }<a name="line.821"></a>
<FONT color="green">822</FONT>            }<a name="line.822"></a>
<FONT color="green">823</FONT>    <a name="line.823"></a>
<FONT color="green">824</FONT>            return result;<a name="line.824"></a>
<FONT color="green">825</FONT>        }<a name="line.825"></a>
<FONT color="green">826</FONT>    <a name="line.826"></a>
<FONT color="green">827</FONT>        /**<a name="line.827"></a>
<FONT color="green">828</FONT>         * Compute a linear combination accurately.<a name="line.828"></a>
<FONT color="green">829</FONT>         * &lt;p&gt;<a name="line.829"></a>
<FONT color="green">830</FONT>         * This method computes a&lt;sub&gt;1&lt;/sub&gt;&amp;times;b&lt;sub&gt;1&lt;/sub&gt; +<a name="line.830"></a>
<FONT color="green">831</FONT>         * a&lt;sub&gt;2&lt;/sub&gt;&amp;times;b&lt;sub&gt;2&lt;/sub&gt; to high accuracy. It does<a name="line.831"></a>
<FONT color="green">832</FONT>         * so by using specific multiplication and addition algorithms to<a name="line.832"></a>
<FONT color="green">833</FONT>         * preserve accuracy and reduce cancellation effects. It is based<a name="line.833"></a>
<FONT color="green">834</FONT>         * on the 2005 paper &lt;a<a name="line.834"></a>
<FONT color="green">835</FONT>         * href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547"&gt;<a name="line.835"></a>
<FONT color="green">836</FONT>         * Accurate Sum and Dot Product&lt;/a&gt; by Takeshi Ogita,<a name="line.836"></a>
<FONT color="green">837</FONT>         * Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.<a name="line.837"></a>
<FONT color="green">838</FONT>         * &lt;/p&gt;<a name="line.838"></a>
<FONT color="green">839</FONT>         * @param a1 first factor of the first term<a name="line.839"></a>
<FONT color="green">840</FONT>         * @param b1 second factor of the first term<a name="line.840"></a>
<FONT color="green">841</FONT>         * @param a2 first factor of the second term<a name="line.841"></a>
<FONT color="green">842</FONT>         * @param b2 second factor of the second term<a name="line.842"></a>
<FONT color="green">843</FONT>         * @return a&lt;sub&gt;1&lt;/sub&gt;&amp;times;b&lt;sub&gt;1&lt;/sub&gt; +<a name="line.843"></a>
<FONT color="green">844</FONT>         * a&lt;sub&gt;2&lt;/sub&gt;&amp;times;b&lt;sub&gt;2&lt;/sub&gt;<a name="line.844"></a>
<FONT color="green">845</FONT>         * @see #linearCombination(double, double, double, double, double, double)<a name="line.845"></a>
<FONT color="green">846</FONT>         * @see #linearCombination(double, double, double, double, double, double, double, double)<a name="line.846"></a>
<FONT color="green">847</FONT>         */<a name="line.847"></a>
<FONT color="green">848</FONT>        public static double linearCombination(final double a1, final double b1,<a name="line.848"></a>
<FONT color="green">849</FONT>                                               final double a2, final double b2) {<a name="line.849"></a>
<FONT color="green">850</FONT>    <a name="line.850"></a>
<FONT color="green">851</FONT>            // the code below is split in many additions/subtractions that may<a name="line.851"></a>
<FONT color="green">852</FONT>            // appear redundant. However, they should NOT be simplified, as they<a name="line.852"></a>
<FONT color="green">853</FONT>            // use IEEE754 floating point arithmetic rounding properties.<a name="line.853"></a>
<FONT color="green">854</FONT>            // as an example, the expression "ca1 - (ca1 - a1)" is NOT the same as "a1"<a name="line.854"></a>
<FONT color="green">855</FONT>            // The variable naming conventions are that xyzHigh contains the most significant<a name="line.855"></a>
<FONT color="green">856</FONT>            // bits of xyz and xyzLow contains its least significant bits. So theoretically<a name="line.856"></a>
<FONT color="green">857</FONT>            // xyz is the sum xyzHigh + xyzLow, but in many cases below, this sum cannot<a name="line.857"></a>
<FONT color="green">858</FONT>            // be represented in only one double precision number so we preserve two numbers<a name="line.858"></a>
<FONT color="green">859</FONT>            // to hold it as long as we can, combining the high and low order bits together<a name="line.859"></a>
<FONT color="green">860</FONT>            // only at the end, after cancellation may have occurred on high order bits<a name="line.860"></a>
<FONT color="green">861</FONT>    <a name="line.861"></a>
<FONT color="green">862</FONT>            // split a1 and b1 as two 26 bits numbers<a name="line.862"></a>
<FONT color="green">863</FONT>            final double ca1        = SPLIT_FACTOR * a1;<a name="line.863"></a>
<FONT color="green">864</FONT>            final double a1High     = ca1 - (ca1 - a1);<a name="line.864"></a>
<FONT color="green">865</FONT>            final double a1Low      = a1 - a1High;<a name="line.865"></a>
<FONT color="green">866</FONT>            final double cb1        = SPLIT_FACTOR * b1;<a name="line.866"></a>
<FONT color="green">867</FONT>            final double b1High     = cb1 - (cb1 - b1);<a name="line.867"></a>
<FONT color="green">868</FONT>            final double b1Low      = b1 - b1High;<a name="line.868"></a>
<FONT color="green">869</FONT>    <a name="line.869"></a>
<FONT color="green">870</FONT>            // accurate multiplication a1 * b1<a name="line.870"></a>
<FONT color="green">871</FONT>            final double prod1High  = a1 * b1;<a name="line.871"></a>
<FONT color="green">872</FONT>            final double prod1Low   = a1Low * b1Low - (((prod1High - a1High * b1High) - a1Low * b1High) - a1High * b1Low);<a name="line.872"></a>
<FONT color="green">873</FONT>    <a name="line.873"></a>
<FONT color="green">874</FONT>            // split a2 and b2 as two 26 bits numbers<a name="line.874"></a>
<FONT color="green">875</FONT>            final double ca2        = SPLIT_FACTOR * a2;<a name="line.875"></a>
<FONT color="green">876</FONT>            final double a2High     = ca2 - (ca2 - a2);<a name="line.876"></a>
<FONT color="green">877</FONT>            final double a2Low      = a2 - a2High;<a name="line.877"></a>
<FONT color="green">878</FONT>            final double cb2        = SPLIT_FACTOR * b2;<a name="line.878"></a>
<FONT color="green">879</FONT>            final double b2High     = cb2 - (cb2 - b2);<a name="line.879"></a>
<FONT color="green">880</FONT>            final double b2Low      = b2 - b2High;<a name="line.880"></a>
<FONT color="green">881</FONT>    <a name="line.881"></a>
<FONT color="green">882</FONT>            // accurate multiplication a2 * b2<a name="line.882"></a>
<FONT color="green">883</FONT>            final double prod2High  = a2 * b2;<a name="line.883"></a>
<FONT color="green">884</FONT>            final double prod2Low   = a2Low * b2Low - (((prod2High - a2High * b2High) - a2Low * b2High) - a2High * b2Low);<a name="line.884"></a>
<FONT color="green">885</FONT>    <a name="line.885"></a>
<FONT color="green">886</FONT>            // accurate addition a1 * b1 + a2 * b2<a name="line.886"></a>
<FONT color="green">887</FONT>            final double s12High    = prod1High + prod2High;<a name="line.887"></a>
<FONT color="green">888</FONT>            final double s12Prime   = s12High - prod2High;<a name="line.888"></a>
<FONT color="green">889</FONT>            final double s12Low     = (prod2High - (s12High - s12Prime)) + (prod1High - s12Prime);<a name="line.889"></a>
<FONT color="green">890</FONT>    <a name="line.890"></a>
<FONT color="green">891</FONT>            // final rounding, s12 may have suffered many cancellations, we try<a name="line.891"></a>
<FONT color="green">892</FONT>            // to recover some bits from the extra words we have saved up to now<a name="line.892"></a>
<FONT color="green">893</FONT>            double result = s12High + (prod1Low + prod2Low + s12Low);<a name="line.893"></a>
<FONT color="green">894</FONT>    <a name="line.894"></a>
<FONT color="green">895</FONT>            if (Double.isNaN(result)) {<a name="line.895"></a>
<FONT color="green">896</FONT>                // either we have split infinite numbers or some coefficients were NaNs,<a name="line.896"></a>
<FONT color="green">897</FONT>                // just rely on the naive implementation and let IEEE754 handle this<a name="line.897"></a>
<FONT color="green">898</FONT>                result = a1 * b1 + a2 * b2;<a name="line.898"></a>
<FONT color="green">899</FONT>            }<a name="line.899"></a>
<FONT color="green">900</FONT>    <a name="line.900"></a>
<FONT color="green">901</FONT>            return result;<a name="line.901"></a>
<FONT color="green">902</FONT>        }<a name="line.902"></a>
<FONT color="green">903</FONT>    <a name="line.903"></a>
<FONT color="green">904</FONT>        /**<a name="line.904"></a>
<FONT color="green">905</FONT>         * Compute a linear combination accurately.<a name="line.905"></a>
<FONT color="green">906</FONT>         * &lt;p&gt;<a name="line.906"></a>
<FONT color="green">907</FONT>         * This method computes a&lt;sub&gt;1&lt;/sub&gt;&amp;times;b&lt;sub&gt;1&lt;/sub&gt; +<a name="line.907"></a>
<FONT color="green">908</FONT>         * a&lt;sub&gt;2&lt;/sub&gt;&amp;times;b&lt;sub&gt;2&lt;/sub&gt; + a&lt;sub&gt;3&lt;/sub&gt;&amp;times;b&lt;sub&gt;3&lt;/sub&gt;<a name="line.908"></a>
<FONT color="green">909</FONT>         * to high accuracy. It does so by using specific multiplication and<a name="line.909"></a>
<FONT color="green">910</FONT>         * addition algorithms to preserve accuracy and reduce cancellation effects.<a name="line.910"></a>
<FONT color="green">911</FONT>         * It is based on the 2005 paper &lt;a<a name="line.911"></a>
<FONT color="green">912</FONT>         * href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547"&gt;<a name="line.912"></a>
<FONT color="green">913</FONT>         * Accurate Sum and Dot Product&lt;/a&gt; by Takeshi Ogita,<a name="line.913"></a>
<FONT color="green">914</FONT>         * Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.<a name="line.914"></a>
<FONT color="green">915</FONT>         * &lt;/p&gt;<a name="line.915"></a>
<FONT color="green">916</FONT>         * @param a1 first factor of the first term<a name="line.916"></a>
<FONT color="green">917</FONT>         * @param b1 second factor of the first term<a name="line.917"></a>
<FONT color="green">918</FONT>         * @param a2 first factor of the second term<a name="line.918"></a>
<FONT color="green">919</FONT>         * @param b2 second factor of the second term<a name="line.919"></a>
<FONT color="green">920</FONT>         * @param a3 first factor of the third term<a name="line.920"></a>
<FONT color="green">921</FONT>         * @param b3 second factor of the third term<a name="line.921"></a>
<FONT color="green">922</FONT>         * @return a&lt;sub&gt;1&lt;/sub&gt;&amp;times;b&lt;sub&gt;1&lt;/sub&gt; +<a name="line.922"></a>
<FONT color="green">923</FONT>         * a&lt;sub&gt;2&lt;/sub&gt;&amp;times;b&lt;sub&gt;2&lt;/sub&gt; + a&lt;sub&gt;3&lt;/sub&gt;&amp;times;b&lt;sub&gt;3&lt;/sub&gt;<a name="line.923"></a>
<FONT color="green">924</FONT>         * @see #linearCombination(double, double, double, double)<a name="line.924"></a>
<FONT color="green">925</FONT>         * @see #linearCombination(double, double, double, double, double, double, double, double)<a name="line.925"></a>
<FONT color="green">926</FONT>         */<a name="line.926"></a>
<FONT color="green">927</FONT>        public static double linearCombination(final double a1, final double b1,<a name="line.927"></a>
<FONT color="green">928</FONT>                                               final double a2, final double b2,<a name="line.928"></a>
<FONT color="green">929</FONT>                                               final double a3, final double b3) {<a name="line.929"></a>
<FONT color="green">930</FONT>    <a name="line.930"></a>
<FONT color="green">931</FONT>            // the code below is split in many additions/subtractions that may<a name="line.931"></a>
<FONT color="green">932</FONT>            // appear redundant. However, they should NOT be simplified, as they<a name="line.932"></a>
<FONT color="green">933</FONT>            // do use IEEE754 floating point arithmetic rounding properties.<a name="line.933"></a>
<FONT color="green">934</FONT>            // as an example, the expression "ca1 - (ca1 - a1)" is NOT the same as "a1"<a name="line.934"></a>
<FONT color="green">935</FONT>            // The variables naming conventions are that xyzHigh contains the most significant<a name="line.935"></a>
<FONT color="green">936</FONT>            // bits of xyz and xyzLow contains its least significant bits. So theoretically<a name="line.936"></a>
<FONT color="green">937</FONT>            // xyz is the sum xyzHigh + xyzLow, but in many cases below, this sum cannot<a name="line.937"></a>
<FONT color="green">938</FONT>            // be represented in only one double precision number so we preserve two numbers<a name="line.938"></a>
<FONT color="green">939</FONT>            // to hold it as long as we can, combining the high and low order bits together<a name="line.939"></a>
<FONT color="green">940</FONT>            // only at the end, after cancellation may have occurred on high order bits<a name="line.940"></a>
<FONT color="green">941</FONT>    <a name="line.941"></a>
<FONT color="green">942</FONT>            // split a1 and b1 as two 26 bits numbers<a name="line.942"></a>
<FONT color="green">943</FONT>            final double ca1        = SPLIT_FACTOR * a1;<a name="line.943"></a>
<FONT color="green">944</FONT>            final double a1High     = ca1 - (ca1 - a1);<a name="line.944"></a>
<FONT color="green">945</FONT>            final double a1Low      = a1 - a1High;<a name="line.945"></a>
<FONT color="green">946</FONT>            final double cb1        = SPLIT_FACTOR * b1;<a name="line.946"></a>
<FONT color="green">947</FONT>            final double b1High     = cb1 - (cb1 - b1);<a name="line.947"></a>
<FONT color="green">948</FONT>            final double b1Low      = b1 - b1High;<a name="line.948"></a>
<FONT color="green">949</FONT>    <a name="line.949"></a>
<FONT color="green">950</FONT>            // accurate multiplication a1 * b1<a name="line.950"></a>
<FONT color="green">951</FONT>            final double prod1High  = a1 * b1;<a name="line.951"></a>
<FONT color="green">952</FONT>            final double prod1Low   = a1Low * b1Low - (((prod1High - a1High * b1High) - a1Low * b1High) - a1High * b1Low);<a name="line.952"></a>
<FONT color="green">953</FONT>    <a name="line.953"></a>
<FONT color="green">954</FONT>            // split a2 and b2 as two 26 bits numbers<a name="line.954"></a>
<FONT color="green">955</FONT>            final double ca2        = SPLIT_FACTOR * a2;<a name="line.955"></a>
<FONT color="green">956</FONT>            final double a2High     = ca2 - (ca2 - a2);<a name="line.956"></a>
<FONT color="green">957</FONT>            final double a2Low      = a2 - a2High;<a name="line.957"></a>
<FONT color="green">958</FONT>            final double cb2        = SPLIT_FACTOR * b2;<a name="line.958"></a>
<FONT color="green">959</FONT>            final double b2High     = cb2 - (cb2 - b2);<a name="line.959"></a>
<FONT color="green">960</FONT>            final double b2Low      = b2 - b2High;<a name="line.960"></a>
<FONT color="green">961</FONT>    <a name="line.961"></a>
<FONT color="green">962</FONT>            // accurate multiplication a2 * b2<a name="line.962"></a>
<FONT color="green">963</FONT>            final double prod2High  = a2 * b2;<a name="line.963"></a>
<FONT color="green">964</FONT>            final double prod2Low   = a2Low * b2Low - (((prod2High - a2High * b2High) - a2Low * b2High) - a2High * b2Low);<a name="line.964"></a>
<FONT color="green">965</FONT>    <a name="line.965"></a>
<FONT color="green">966</FONT>            // split a3 and b3 as two 26 bits numbers<a name="line.966"></a>
<FONT color="green">967</FONT>            final double ca3        = SPLIT_FACTOR * a3;<a name="line.967"></a>
<FONT color="green">968</FONT>            final double a3High     = ca3 - (ca3 - a3);<a name="line.968"></a>
<FONT color="green">969</FONT>            final double a3Low      = a3 - a3High;<a name="line.969"></a>
<FONT color="green">970</FONT>            final double cb3        = SPLIT_FACTOR * b3;<a name="line.970"></a>
<FONT color="green">971</FONT>            final double b3High     = cb3 - (cb3 - b3);<a name="line.971"></a>
<FONT color="green">972</FONT>            final double b3Low      = b3 - b3High;<a name="line.972"></a>
<FONT color="green">973</FONT>    <a name="line.973"></a>
<FONT color="green">974</FONT>            // accurate multiplication a3 * b3<a name="line.974"></a>
<FONT color="green">975</FONT>            final double prod3High  = a3 * b3;<a name="line.975"></a>
<FONT color="green">976</FONT>            final double prod3Low   = a3Low * b3Low - (((prod3High - a3High * b3High) - a3Low * b3High) - a3High * b3Low);<a name="line.976"></a>
<FONT color="green">977</FONT>    <a name="line.977"></a>
<FONT color="green">978</FONT>            // accurate addition a1 * b1 + a2 * b2<a name="line.978"></a>
<FONT color="green">979</FONT>            final double s12High    = prod1High + prod2High;<a name="line.979"></a>
<FONT color="green">980</FONT>            final double s12Prime   = s12High - prod2High;<a name="line.980"></a>
<FONT color="green">981</FONT>            final double s12Low     = (prod2High - (s12High - s12Prime)) + (prod1High - s12Prime);<a name="line.981"></a>
<FONT color="green">982</FONT>    <a name="line.982"></a>
<FONT color="green">983</FONT>            // accurate addition a1 * b1 + a2 * b2 + a3 * b3<a name="line.983"></a>
<FONT color="green">984</FONT>            final double s123High   = s12High + prod3High;<a name="line.984"></a>
<FONT color="green">985</FONT>            final double s123Prime  = s123High - prod3High;<a name="line.985"></a>
<FONT color="green">986</FONT>            final double s123Low    = (prod3High - (s123High - s123Prime)) + (s12High - s123Prime);<a name="line.986"></a>
<FONT color="green">987</FONT>    <a name="line.987"></a>
<FONT color="green">988</FONT>            // final rounding, s123 may have suffered many cancellations, we try<a name="line.988"></a>
<FONT color="green">989</FONT>            // to recover some bits from the extra words we have saved up to now<a name="line.989"></a>
<FONT color="green">990</FONT>            double result = s123High + (prod1Low + prod2Low + prod3Low + s12Low + s123Low);<a name="line.990"></a>
<FONT color="green">991</FONT>    <a name="line.991"></a>
<FONT color="green">992</FONT>            if (Double.isNaN(result)) {<a name="line.992"></a>
<FONT color="green">993</FONT>                // either we have split infinite numbers or some coefficients were NaNs,<a name="line.993"></a>
<FONT color="green">994</FONT>                // just rely on the naive implementation and let IEEE754 handle this<a name="line.994"></a>
<FONT color="green">995</FONT>                result = a1 * b1 + a2 * b2 + a3 * b3;<a name="line.995"></a>
<FONT color="green">996</FONT>            }<a name="line.996"></a>
<FONT color="green">997</FONT>    <a name="line.997"></a>
<FONT color="green">998</FONT>            return result;<a name="line.998"></a>
<FONT color="green">999</FONT>        }<a name="line.999"></a>
<FONT color="green">1000</FONT>    <a name="line.1000"></a>
<FONT color="green">1001</FONT>        /**<a name="line.1001"></a>
<FONT color="green">1002</FONT>         * Compute a linear combination accurately.<a name="line.1002"></a>
<FONT color="green">1003</FONT>         * &lt;p&gt;<a name="line.1003"></a>
<FONT color="green">1004</FONT>         * This method computes a&lt;sub&gt;1&lt;/sub&gt;&amp;times;b&lt;sub&gt;1&lt;/sub&gt; +<a name="line.1004"></a>
<FONT color="green">1005</FONT>         * a&lt;sub&gt;2&lt;/sub&gt;&amp;times;b&lt;sub&gt;2&lt;/sub&gt; + a&lt;sub&gt;3&lt;/sub&gt;&amp;times;b&lt;sub&gt;3&lt;/sub&gt; +<a name="line.1005"></a>
<FONT color="green">1006</FONT>         * a&lt;sub&gt;4&lt;/sub&gt;&amp;times;b&lt;sub&gt;4&lt;/sub&gt;<a name="line.1006"></a>
<FONT color="green">1007</FONT>         * to high accuracy. It does so by using specific multiplication and<a name="line.1007"></a>
<FONT color="green">1008</FONT>         * addition algorithms to preserve accuracy and reduce cancellation effects.<a name="line.1008"></a>
<FONT color="green">1009</FONT>         * It is based on the 2005 paper &lt;a<a name="line.1009"></a>
<FONT color="green">1010</FONT>         * href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547"&gt;<a name="line.1010"></a>
<FONT color="green">1011</FONT>         * Accurate Sum and Dot Product&lt;/a&gt; by Takeshi Ogita,<a name="line.1011"></a>
<FONT color="green">1012</FONT>         * Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.<a name="line.1012"></a>
<FONT color="green">1013</FONT>         * &lt;/p&gt;<a name="line.1013"></a>
<FONT color="green">1014</FONT>         * @param a1 first factor of the first term<a name="line.1014"></a>
<FONT color="green">1015</FONT>         * @param b1 second factor of the first term<a name="line.1015"></a>
<FONT color="green">1016</FONT>         * @param a2 first factor of the second term<a name="line.1016"></a>
<FONT color="green">1017</FONT>         * @param b2 second factor of the second term<a name="line.1017"></a>
<FONT color="green">1018</FONT>         * @param a3 first factor of the third term<a name="line.1018"></a>
<FONT color="green">1019</FONT>         * @param b3 second factor of the third term<a name="line.1019"></a>
<FONT color="green">1020</FONT>         * @param a4 first factor of the third term<a name="line.1020"></a>
<FONT color="green">1021</FONT>         * @param b4 second factor of the third term<a name="line.1021"></a>
<FONT color="green">1022</FONT>         * @return a&lt;sub&gt;1&lt;/sub&gt;&amp;times;b&lt;sub&gt;1&lt;/sub&gt; +<a name="line.1022"></a>
<FONT color="green">1023</FONT>         * a&lt;sub&gt;2&lt;/sub&gt;&amp;times;b&lt;sub&gt;2&lt;/sub&gt; + a&lt;sub&gt;3&lt;/sub&gt;&amp;times;b&lt;sub&gt;3&lt;/sub&gt; +<a name="line.1023"></a>
<FONT color="green">1024</FONT>         * a&lt;sub&gt;4&lt;/sub&gt;&amp;times;b&lt;sub&gt;4&lt;/sub&gt;<a name="line.1024"></a>
<FONT color="green">1025</FONT>         * @see #linearCombination(double, double, double, double)<a name="line.1025"></a>
<FONT color="green">1026</FONT>         * @see #linearCombination(double, double, double, double, double, double)<a name="line.1026"></a>
<FONT color="green">1027</FONT>         */<a name="line.1027"></a>
<FONT color="green">1028</FONT>        public static double linearCombination(final double a1, final double b1,<a name="line.1028"></a>
<FONT color="green">1029</FONT>                                               final double a2, final double b2,<a name="line.1029"></a>
<FONT color="green">1030</FONT>                                               final double a3, final double b3,<a name="line.1030"></a>
<FONT color="green">1031</FONT>                                               final double a4, final double b4) {<a name="line.1031"></a>
<FONT color="green">1032</FONT>    <a name="line.1032"></a>
<FONT color="green">1033</FONT>            // the code below is split in many additions/subtractions that may<a name="line.1033"></a>
<FONT color="green">1034</FONT>            // appear redundant. However, they should NOT be simplified, as they<a name="line.1034"></a>
<FONT color="green">1035</FONT>            // do use IEEE754 floating point arithmetic rounding properties.<a name="line.1035"></a>
<FONT color="green">1036</FONT>            // as an example, the expression "ca1 - (ca1 - a1)" is NOT the same as "a1"<a name="line.1036"></a>
<FONT color="green">1037</FONT>            // The variables naming conventions are that xyzHigh contains the most significant<a name="line.1037"></a>
<FONT color="green">1038</FONT>            // bits of xyz and xyzLow contains its least significant bits. So theoretically<a name="line.1038"></a>
<FONT color="green">1039</FONT>            // xyz is the sum xyzHigh + xyzLow, but in many cases below, this sum cannot<a name="line.1039"></a>
<FONT color="green">1040</FONT>            // be represented in only one double precision number so we preserve two numbers<a name="line.1040"></a>
<FONT color="green">1041</FONT>            // to hold it as long as we can, combining the high and low order bits together<a name="line.1041"></a>
<FONT color="green">1042</FONT>            // only at the end, after cancellation may have occurred on high order bits<a name="line.1042"></a>
<FONT color="green">1043</FONT>    <a name="line.1043"></a>
<FONT color="green">1044</FONT>            // split a1 and b1 as two 26 bits numbers<a name="line.1044"></a>
<FONT color="green">1045</FONT>            final double ca1        = SPLIT_FACTOR * a1;<a name="line.1045"></a>
<FONT color="green">1046</FONT>            final double a1High     = ca1 - (ca1 - a1);<a name="line.1046"></a>
<FONT color="green">1047</FONT>            final double a1Low      = a1 - a1High;<a name="line.1047"></a>
<FONT color="green">1048</FONT>            final double cb1        = SPLIT_FACTOR * b1;<a name="line.1048"></a>
<FONT color="green">1049</FONT>            final double b1High     = cb1 - (cb1 - b1);<a name="line.1049"></a>
<FONT color="green">1050</FONT>            final double b1Low      = b1 - b1High;<a name="line.1050"></a>
<FONT color="green">1051</FONT>    <a name="line.1051"></a>
<FONT color="green">1052</FONT>            // accurate multiplication a1 * b1<a name="line.1052"></a>
<FONT color="green">1053</FONT>            final double prod1High  = a1 * b1;<a name="line.1053"></a>
<FONT color="green">1054</FONT>            final double prod1Low   = a1Low * b1Low - (((prod1High - a1High * b1High) - a1Low * b1High) - a1High * b1Low);<a name="line.1054"></a>
<FONT color="green">1055</FONT>    <a name="line.1055"></a>
<FONT color="green">1056</FONT>            // split a2 and b2 as two 26 bits numbers<a name="line.1056"></a>
<FONT color="green">1057</FONT>            final double ca2        = SPLIT_FACTOR * a2;<a name="line.1057"></a>
<FONT color="green">1058</FONT>            final double a2High     = ca2 - (ca2 - a2);<a name="line.1058"></a>
<FONT color="green">1059</FONT>            final double a2Low      = a2 - a2High;<a name="line.1059"></a>
<FONT color="green">1060</FONT>            final double cb2        = SPLIT_FACTOR * b2;<a name="line.1060"></a>
<FONT color="green">1061</FONT>            final double b2High     = cb2 - (cb2 - b2);<a name="line.1061"></a>
<FONT color="green">1062</FONT>            final double b2Low      = b2 - b2High;<a name="line.1062"></a>
<FONT color="green">1063</FONT>    <a name="line.1063"></a>
<FONT color="green">1064</FONT>            // accurate multiplication a2 * b2<a name="line.1064"></a>
<FONT color="green">1065</FONT>            final double prod2High  = a2 * b2;<a name="line.1065"></a>
<FONT color="green">1066</FONT>            final double prod2Low   = a2Low * b2Low - (((prod2High - a2High * b2High) - a2Low * b2High) - a2High * b2Low);<a name="line.1066"></a>
<FONT color="green">1067</FONT>    <a name="line.1067"></a>
<FONT color="green">1068</FONT>            // split a3 and b3 as two 26 bits numbers<a name="line.1068"></a>
<FONT color="green">1069</FONT>            final double ca3        = SPLIT_FACTOR * a3;<a name="line.1069"></a>
<FONT color="green">1070</FONT>            final double a3High     = ca3 - (ca3 - a3);<a name="line.1070"></a>
<FONT color="green">1071</FONT>            final double a3Low      = a3 - a3High;<a name="line.1071"></a>
<FONT color="green">1072</FONT>            final double cb3        = SPLIT_FACTOR * b3;<a name="line.1072"></a>
<FONT color="green">1073</FONT>            final double b3High     = cb3 - (cb3 - b3);<a name="line.1073"></a>
<FONT color="green">1074</FONT>            final double b3Low      = b3 - b3High;<a name="line.1074"></a>
<FONT color="green">1075</FONT>    <a name="line.1075"></a>
<FONT color="green">1076</FONT>            // accurate multiplication a3 * b3<a name="line.1076"></a>
<FONT color="green">1077</FONT>            final double prod3High  = a3 * b3;<a name="line.1077"></a>
<FONT color="green">1078</FONT>            final double prod3Low   = a3Low * b3Low - (((prod3High - a3High * b3High) - a3Low * b3High) - a3High * b3Low);<a name="line.1078"></a>
<FONT color="green">1079</FONT>    <a name="line.1079"></a>
<FONT color="green">1080</FONT>            // split a4 and b4 as two 26 bits numbers<a name="line.1080"></a>
<FONT color="green">1081</FONT>            final double ca4        = SPLIT_FACTOR * a4;<a name="line.1081"></a>
<FONT color="green">1082</FONT>            final double a4High     = ca4 - (ca4 - a4);<a name="line.1082"></a>
<FONT color="green">1083</FONT>            final double a4Low      = a4 - a4High;<a name="line.1083"></a>
<FONT color="green">1084</FONT>            final double cb4        = SPLIT_FACTOR * b4;<a name="line.1084"></a>
<FONT color="green">1085</FONT>            final double b4High     = cb4 - (cb4 - b4);<a name="line.1085"></a>
<FONT color="green">1086</FONT>            final double b4Low      = b4 - b4High;<a name="line.1086"></a>
<FONT color="green">1087</FONT>    <a name="line.1087"></a>
<FONT color="green">1088</FONT>            // accurate multiplication a4 * b4<a name="line.1088"></a>
<FONT color="green">1089</FONT>            final double prod4High  = a4 * b4;<a name="line.1089"></a>
<FONT color="green">1090</FONT>            final double prod4Low   = a4Low * b4Low - (((prod4High - a4High * b4High) - a4Low * b4High) - a4High * b4Low);<a name="line.1090"></a>
<FONT color="green">1091</FONT>    <a name="line.1091"></a>
<FONT color="green">1092</FONT>            // accurate addition a1 * b1 + a2 * b2<a name="line.1092"></a>
<FONT color="green">1093</FONT>            final double s12High    = prod1High + prod2High;<a name="line.1093"></a>
<FONT color="green">1094</FONT>            final double s12Prime   = s12High - prod2High;<a name="line.1094"></a>
<FONT color="green">1095</FONT>            final double s12Low     = (prod2High - (s12High - s12Prime)) + (prod1High - s12Prime);<a name="line.1095"></a>
<FONT color="green">1096</FONT>    <a name="line.1096"></a>
<FONT color="green">1097</FONT>            // accurate addition a1 * b1 + a2 * b2 + a3 * b3<a name="line.1097"></a>
<FONT color="green">1098</FONT>            final double s123High   = s12High + prod3High;<a name="line.1098"></a>
<FONT color="green">1099</FONT>            final double s123Prime  = s123High - prod3High;<a name="line.1099"></a>
<FONT color="green">1100</FONT>            final double s123Low    = (prod3High - (s123High - s123Prime)) + (s12High - s123Prime);<a name="line.1100"></a>
<FONT color="green">1101</FONT>    <a name="line.1101"></a>
<FONT color="green">1102</FONT>            // accurate addition a1 * b1 + a2 * b2 + a3 * b3 + a4 * b4<a name="line.1102"></a>
<FONT color="green">1103</FONT>            final double s1234High  = s123High + prod4High;<a name="line.1103"></a>
<FONT color="green">1104</FONT>            final double s1234Prime = s1234High - prod4High;<a name="line.1104"></a>
<FONT color="green">1105</FONT>            final double s1234Low   = (prod4High - (s1234High - s1234Prime)) + (s123High - s1234Prime);<a name="line.1105"></a>
<FONT color="green">1106</FONT>    <a name="line.1106"></a>
<FONT color="green">1107</FONT>            // final rounding, s1234 may have suffered many cancellations, we try<a name="line.1107"></a>
<FONT color="green">1108</FONT>            // to recover some bits from the extra words we have saved up to now<a name="line.1108"></a>
<FONT color="green">1109</FONT>            double result = s1234High + (prod1Low + prod2Low + prod3Low + prod4Low + s12Low + s123Low + s1234Low);<a name="line.1109"></a>
<FONT color="green">1110</FONT>    <a name="line.1110"></a>
<FONT color="green">1111</FONT>            if (Double.isNaN(result)) {<a name="line.1111"></a>
<FONT color="green">1112</FONT>                // either we have split infinite numbers or some coefficients were NaNs,<a name="line.1112"></a>
<FONT color="green">1113</FONT>                // just rely on the naive implementation and let IEEE754 handle this<a name="line.1113"></a>
<FONT color="green">1114</FONT>                result = a1 * b1 + a2 * b2 + a3 * b3 + a4 * b4;<a name="line.1114"></a>
<FONT color="green">1115</FONT>            }<a name="line.1115"></a>
<FONT color="green">1116</FONT>    <a name="line.1116"></a>
<FONT color="green">1117</FONT>            return result;<a name="line.1117"></a>
<FONT color="green">1118</FONT>        }<a name="line.1118"></a>
<FONT color="green">1119</FONT>    <a name="line.1119"></a>
<FONT color="green">1120</FONT>        /**<a name="line.1120"></a>
<FONT color="green">1121</FONT>         * Returns true iff both arguments are null or have same dimensions and all<a name="line.1121"></a>
<FONT color="green">1122</FONT>         * their elements are equal as defined by<a name="line.1122"></a>
<FONT color="green">1123</FONT>         * {@link Precision#equals(float,float)}.<a name="line.1123"></a>
<FONT color="green">1124</FONT>         *<a name="line.1124"></a>
<FONT color="green">1125</FONT>         * @param x first array<a name="line.1125"></a>
<FONT color="green">1126</FONT>         * @param y second array<a name="line.1126"></a>
<FONT color="green">1127</FONT>         * @return true if the values are both null or have same dimension<a name="line.1127"></a>
<FONT color="green">1128</FONT>         * and equal elements.<a name="line.1128"></a>
<FONT color="green">1129</FONT>         */<a name="line.1129"></a>
<FONT color="green">1130</FONT>        public static boolean equals(float[] x, float[] y) {<a name="line.1130"></a>
<FONT color="green">1131</FONT>            if ((x == null) || (y == null)) {<a name="line.1131"></a>
<FONT color="green">1132</FONT>                return !((x == null) ^ (y == null));<a name="line.1132"></a>
<FONT color="green">1133</FONT>            }<a name="line.1133"></a>
<FONT color="green">1134</FONT>            if (x.length != y.length) {<a name="line.1134"></a>
<FONT color="green">1135</FONT>                return false;<a name="line.1135"></a>
<FONT color="green">1136</FONT>            }<a name="line.1136"></a>
<FONT color="green">1137</FONT>            for (int i = 0; i &lt; x.length; ++i) {<a name="line.1137"></a>
<FONT color="green">1138</FONT>                if (!Precision.equals(x[i], y[i])) {<a name="line.1138"></a>
<FONT color="green">1139</FONT>                    return false;<a name="line.1139"></a>
<FONT color="green">1140</FONT>                }<a name="line.1140"></a>
<FONT color="green">1141</FONT>            }<a name="line.1141"></a>
<FONT color="green">1142</FONT>            return true;<a name="line.1142"></a>
<FONT color="green">1143</FONT>        }<a name="line.1143"></a>
<FONT color="green">1144</FONT>    <a name="line.1144"></a>
<FONT color="green">1145</FONT>        /**<a name="line.1145"></a>
<FONT color="green">1146</FONT>         * Returns true iff both arguments are null or have same dimensions and all<a name="line.1146"></a>
<FONT color="green">1147</FONT>         * their elements are equal as defined by<a name="line.1147"></a>
<FONT color="green">1148</FONT>         * {@link Precision#equalsIncludingNaN(double,double) this method}.<a name="line.1148"></a>
<FONT color="green">1149</FONT>         *<a name="line.1149"></a>
<FONT color="green">1150</FONT>         * @param x first array<a name="line.1150"></a>
<FONT color="green">1151</FONT>         * @param y second array<a name="line.1151"></a>
<FONT color="green">1152</FONT>         * @return true if the values are both null or have same dimension and<a name="line.1152"></a>
<FONT color="green">1153</FONT>         * equal elements<a name="line.1153"></a>
<FONT color="green">1154</FONT>         * @since 2.2<a name="line.1154"></a>
<FONT color="green">1155</FONT>         */<a name="line.1155"></a>
<FONT color="green">1156</FONT>        public static boolean equalsIncludingNaN(float[] x, float[] y) {<a name="line.1156"></a>
<FONT color="green">1157</FONT>            if ((x == null) || (y == null)) {<a name="line.1157"></a>
<FONT color="green">1158</FONT>                return !((x == null) ^ (y == null));<a name="line.1158"></a>
<FONT color="green">1159</FONT>            }<a name="line.1159"></a>
<FONT color="green">1160</FONT>            if (x.length != y.length) {<a name="line.1160"></a>
<FONT color="green">1161</FONT>                return false;<a name="line.1161"></a>
<FONT color="green">1162</FONT>            }<a name="line.1162"></a>
<FONT color="green">1163</FONT>            for (int i = 0; i &lt; x.length; ++i) {<a name="line.1163"></a>
<FONT color="green">1164</FONT>                if (!Precision.equalsIncludingNaN(x[i], y[i])) {<a name="line.1164"></a>
<FONT color="green">1165</FONT>                    return false;<a name="line.1165"></a>
<FONT color="green">1166</FONT>                }<a name="line.1166"></a>
<FONT color="green">1167</FONT>            }<a name="line.1167"></a>
<FONT color="green">1168</FONT>            return true;<a name="line.1168"></a>
<FONT color="green">1169</FONT>        }<a name="line.1169"></a>
<FONT color="green">1170</FONT>    <a name="line.1170"></a>
<FONT color="green">1171</FONT>        /**<a name="line.1171"></a>
<FONT color="green">1172</FONT>         * Returns {@code true} iff both arguments are {@code null} or have same<a name="line.1172"></a>
<FONT color="green">1173</FONT>         * dimensions and all their elements are equal as defined by<a name="line.1173"></a>
<FONT color="green">1174</FONT>         * {@link Precision#equals(double,double)}.<a name="line.1174"></a>
<FONT color="green">1175</FONT>         *<a name="line.1175"></a>
<FONT color="green">1176</FONT>         * @param x First array.<a name="line.1176"></a>
<FONT color="green">1177</FONT>         * @param y Second array.<a name="line.1177"></a>
<FONT color="green">1178</FONT>         * @return {@code true} if the values are both {@code null} or have same<a name="line.1178"></a>
<FONT color="green">1179</FONT>         * dimension and equal elements.<a name="line.1179"></a>
<FONT color="green">1180</FONT>         */<a name="line.1180"></a>
<FONT color="green">1181</FONT>        public static boolean equals(double[] x, double[] y) {<a name="line.1181"></a>
<FONT color="green">1182</FONT>            if ((x == null) || (y == null)) {<a name="line.1182"></a>
<FONT color="green">1183</FONT>                return !((x == null) ^ (y == null));<a name="line.1183"></a>
<FONT color="green">1184</FONT>            }<a name="line.1184"></a>
<FONT color="green">1185</FONT>            if (x.length != y.length) {<a name="line.1185"></a>
<FONT color="green">1186</FONT>                return false;<a name="line.1186"></a>
<FONT color="green">1187</FONT>            }<a name="line.1187"></a>
<FONT color="green">1188</FONT>            for (int i = 0; i &lt; x.length; ++i) {<a name="line.1188"></a>
<FONT color="green">1189</FONT>                if (!Precision.equals(x[i], y[i])) {<a name="line.1189"></a>
<FONT color="green">1190</FONT>                    return false;<a name="line.1190"></a>
<FONT color="green">1191</FONT>                }<a name="line.1191"></a>
<FONT color="green">1192</FONT>            }<a name="line.1192"></a>
<FONT color="green">1193</FONT>            return true;<a name="line.1193"></a>
<FONT color="green">1194</FONT>        }<a name="line.1194"></a>
<FONT color="green">1195</FONT>    <a name="line.1195"></a>
<FONT color="green">1196</FONT>        /**<a name="line.1196"></a>
<FONT color="green">1197</FONT>         * Returns {@code true} iff both arguments are {@code null} or have same<a name="line.1197"></a>
<FONT color="green">1198</FONT>         * dimensions and all their elements are equal as defined by<a name="line.1198"></a>
<FONT color="green">1199</FONT>         * {@link Precision#equalsIncludingNaN(double,double) this method}.<a name="line.1199"></a>
<FONT color="green">1200</FONT>         *<a name="line.1200"></a>
<FONT color="green">1201</FONT>         * @param x First array.<a name="line.1201"></a>
<FONT color="green">1202</FONT>         * @param y Second array.<a name="line.1202"></a>
<FONT color="green">1203</FONT>         * @return {@code true} if the values are both {@code null} or have same<a name="line.1203"></a>
<FONT color="green">1204</FONT>         * dimension and equal elements.<a name="line.1204"></a>
<FONT color="green">1205</FONT>         * @since 2.2<a name="line.1205"></a>
<FONT color="green">1206</FONT>         */<a name="line.1206"></a>
<FONT color="green">1207</FONT>        public static boolean equalsIncludingNaN(double[] x, double[] y) {<a name="line.1207"></a>
<FONT color="green">1208</FONT>            if ((x == null) || (y == null)) {<a name="line.1208"></a>
<FONT color="green">1209</FONT>                return !((x == null) ^ (y == null));<a name="line.1209"></a>
<FONT color="green">1210</FONT>            }<a name="line.1210"></a>
<FONT color="green">1211</FONT>            if (x.length != y.length) {<a name="line.1211"></a>
<FONT color="green">1212</FONT>                return false;<a name="line.1212"></a>
<FONT color="green">1213</FONT>            }<a name="line.1213"></a>
<FONT color="green">1214</FONT>            for (int i = 0; i &lt; x.length; ++i) {<a name="line.1214"></a>
<FONT color="green">1215</FONT>                if (!Precision.equalsIncludingNaN(x[i], y[i])) {<a name="line.1215"></a>
<FONT color="green">1216</FONT>                    return false;<a name="line.1216"></a>
<FONT color="green">1217</FONT>                }<a name="line.1217"></a>
<FONT color="green">1218</FONT>            }<a name="line.1218"></a>
<FONT color="green">1219</FONT>            return true;<a name="line.1219"></a>
<FONT color="green">1220</FONT>        }<a name="line.1220"></a>
<FONT color="green">1221</FONT>    <a name="line.1221"></a>
<FONT color="green">1222</FONT>         /**<a name="line.1222"></a>
<FONT color="green">1223</FONT>          * Normalizes an array to make it sum to a specified value.<a name="line.1223"></a>
<FONT color="green">1224</FONT>          * Returns the result of the transformation &lt;pre&gt;<a name="line.1224"></a>
<FONT color="green">1225</FONT>          *    x |-&gt; x * normalizedSum / sum<a name="line.1225"></a>
<FONT color="green">1226</FONT>          * &lt;/pre&gt;<a name="line.1226"></a>
<FONT color="green">1227</FONT>          * applied to each non-NaN element x of the input array, where sum is the<a name="line.1227"></a>
<FONT color="green">1228</FONT>          * sum of the non-NaN entries in the input array.&lt;/p&gt;<a name="line.1228"></a>
<FONT color="green">1229</FONT>          *<a name="line.1229"></a>
<FONT color="green">1230</FONT>          * &lt;p&gt;Throws IllegalArgumentException if {@code normalizedSum} is infinite<a name="line.1230"></a>
<FONT color="green">1231</FONT>          * or NaN and ArithmeticException if the input array contains any infinite elements<a name="line.1231"></a>
<FONT color="green">1232</FONT>          * or sums to 0.&lt;/p&gt;<a name="line.1232"></a>
<FONT color="green">1233</FONT>          *<a name="line.1233"></a>
<FONT color="green">1234</FONT>          * &lt;p&gt;Ignores (i.e., copies unchanged to the output array) NaNs in the input array.&lt;/p&gt;<a name="line.1234"></a>
<FONT color="green">1235</FONT>          *<a name="line.1235"></a>
<FONT color="green">1236</FONT>          * @param values Input array to be normalized<a name="line.1236"></a>
<FONT color="green">1237</FONT>          * @param normalizedSum Target sum for the normalized array<a name="line.1237"></a>
<FONT color="green">1238</FONT>          * @return the normalized array.<a name="line.1238"></a>
<FONT color="green">1239</FONT>          * @throws MathArithmeticException if the input array contains infinite<a name="line.1239"></a>
<FONT color="green">1240</FONT>          * elements or sums to zero.<a name="line.1240"></a>
<FONT color="green">1241</FONT>          * @throws MathIllegalArgumentException if the target sum is infinite or {@code NaN}.<a name="line.1241"></a>
<FONT color="green">1242</FONT>          * @since 2.1<a name="line.1242"></a>
<FONT color="green">1243</FONT>          */<a name="line.1243"></a>
<FONT color="green">1244</FONT>         public static double[] normalizeArray(double[] values, double normalizedSum)<a name="line.1244"></a>
<FONT color="green">1245</FONT>             throws MathIllegalArgumentException, MathArithmeticException {<a name="line.1245"></a>
<FONT color="green">1246</FONT>             if (Double.isInfinite(normalizedSum)) {<a name="line.1246"></a>
<FONT color="green">1247</FONT>                 throw new MathIllegalArgumentException(LocalizedFormats.NORMALIZE_INFINITE);<a name="line.1247"></a>
<FONT color="green">1248</FONT>             }<a name="line.1248"></a>
<FONT color="green">1249</FONT>             if (Double.isNaN(normalizedSum)) {<a name="line.1249"></a>
<FONT color="green">1250</FONT>                 throw new MathIllegalArgumentException(LocalizedFormats.NORMALIZE_NAN);<a name="line.1250"></a>
<FONT color="green">1251</FONT>             }<a name="line.1251"></a>
<FONT color="green">1252</FONT>             double sum = 0d;<a name="line.1252"></a>
<FONT color="green">1253</FONT>             final int len = values.length;<a name="line.1253"></a>
<FONT color="green">1254</FONT>             double[] out = new double[len];<a name="line.1254"></a>
<FONT color="green">1255</FONT>             for (int i = 0; i &lt; len; i++) {<a name="line.1255"></a>
<FONT color="green">1256</FONT>                 if (Double.isInfinite(values[i])) {<a name="line.1256"></a>
<FONT color="green">1257</FONT>                     throw new MathIllegalArgumentException(LocalizedFormats.INFINITE_ARRAY_ELEMENT, values[i], i);<a name="line.1257"></a>
<FONT color="green">1258</FONT>                 }<a name="line.1258"></a>
<FONT color="green">1259</FONT>                 if (!Double.isNaN(values[i])) {<a name="line.1259"></a>
<FONT color="green">1260</FONT>                     sum += values[i];<a name="line.1260"></a>
<FONT color="green">1261</FONT>                 }<a name="line.1261"></a>
<FONT color="green">1262</FONT>             }<a name="line.1262"></a>
<FONT color="green">1263</FONT>             if (sum == 0) {<a name="line.1263"></a>
<FONT color="green">1264</FONT>                 throw new MathArithmeticException(LocalizedFormats.ARRAY_SUMS_TO_ZERO);<a name="line.1264"></a>
<FONT color="green">1265</FONT>             }<a name="line.1265"></a>
<FONT color="green">1266</FONT>             for (int i = 0; i &lt; len; i++) {<a name="line.1266"></a>
<FONT color="green">1267</FONT>                 if (Double.isNaN(values[i])) {<a name="line.1267"></a>
<FONT color="green">1268</FONT>                     out[i] = Double.NaN;<a name="line.1268"></a>
<FONT color="green">1269</FONT>                 } else {<a name="line.1269"></a>
<FONT color="green">1270</FONT>                     out[i] = values[i] * normalizedSum / sum;<a name="line.1270"></a>
<FONT color="green">1271</FONT>                 }<a name="line.1271"></a>
<FONT color="green">1272</FONT>             }<a name="line.1272"></a>
<FONT color="green">1273</FONT>             return out;<a name="line.1273"></a>
<FONT color="green">1274</FONT>         }<a name="line.1274"></a>
<FONT color="green">1275</FONT>    }<a name="line.1275"></a>




























































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